### MARIA ALESSANDRA RAGUSA

Professor

Mathematical Analysis

Catania University

Catania, Italy

###### Biography

Born June 18th, 1966, degree in Mathematics on July 12th 1988, 110/110 cum laude. In 1989 she become Teaching Assistant in Mathematical Analysis in

Faculty of Engineering of Catania University. In January 1990 she supports the entrance examination to the doctoral program Research in Mathematics,

V cycle, at Catania University, resulting among the winners. In December 1992 she wins a competition exam for Assistant Professor of Mathematical Analysis in Catania University. In June 18th, 2012 PhD in Mathematics at Lule˚a University (Sweden). In January 2000 she wins a competition exam for Associate Professor

of Mathematical Analysis in Catania. In June 2013 she obtained the national scientific qualification for Full Professor of Mathematical Analysis. In October 2017 she becomes Full Professor of Mathematical Analysis in Catania University. Is a member of the international association ”Women in Mathematics”. Winner of the ”Una Tantum” of Catania University, incentive award for academic and scientific merit.

###### Research Interest

###### Scientific Activities

Member of the international association ”Women in Mathematics”. Winner of the ”Una Tantum” of Catania University, incentive award for academic and scientific merit.

###### Publications

1) Commutators and Morrey Spaces (in coll. G. Di Fazio), Bollettino Unione Matematica Italiana, serie VII (V) - A n.3 323–332, (1991).6

2) Interior estimates in Morrey spaces for strong solutions to non divergence form equations with discontinuous coefficients (in coll. G. Di Fazio), Journal of Functional Analysis, 112(2) 241–256, (1993).

3) Interior estimates for strong solutions in Morrey Spaces for elliptic equations, Proceedings of XIV Congresso U.M.I. (1991).

4) A new approach to some trace theorems, Le Matematiche, XLVIII Fasc II, 323–330, (1993).

5) Regularity for weak solutions to the Dirichlet problem in Morrey space, Rivista Mat. Univ. Parma, (5) 3 355–369, (1994).

6) Continuit´a delle soluzioni di equazioni ellittiche quasilineari, Proceedings of XV Congresso U.M.I. (1995).

7) An Adams’ type inequality (in coll. P. Zamboni), Comptes Rendus de l’Acad. Bulg. des Sciences, 50 (4), 13–16, (1997).

8) On Morrey’s regularity of strong solutions to elliptic boundary value problems (in coll. G. Di Fazio, D.K. Palagachev), Comptes Rendus de

l’Academie Bulg. des Sciences, tome 50, (7) 11–14, (1997).

9) Dirichlet Problem in Morrey Spaces for elliptic equations in non divergence form with VMO coefficients, Proceedings of the Eighth International Colloquium on Differential Equations, 385–390, (1998).

10) Sobolev-Morrey spaces related to an ultraparabolic equation (in coll.S. Polidoro), Manuscripta Mathematica, 96, 371–392, (1998).

11) Regularity of solutions of divergence form elliptic equations, Proceedings of the American Mathematical Society, 128 (2), 533–540, (1999).

12) Oblique derivative problem in Morrey spaces ( in coll. D. K. Palagachev) Proceedings of the Nineth International Colloquium on Differential Equations, 307–310, 1999.

13) Regularity of the first derivatives of the solutions of a class of linear elliptic equations of second order with discontinuous coefficients Proceedings of the Nineth International Colloquium on Differential Equations, 337–342, 1999.

14) Global Morrey regularity of strong solutions to Dirichlet problem for elliptic equations with discontinuous coefficients (in coll. G. Di Fazio, D.K.Palagachev), Journal of Functional Analysis, 166, 179–196, (1999).

15) Local regularity of solutions to quasilinear elliptic equations with general structure (in coll. P. Zamboni), Communications in Applied Analysis, 3 (1), 131–147, (1999).

16) Solvability of the Dirichlet problem in H 1,p,λ0 (Ω) for a class of linear second order elliptic partial differential equations, Proceedings of EQUADIFF99, 1, 609–611, (1999).

17) On the L p−estimates for the weak solution of divergence form elliptic equations, Int. Journal of Differential Equations and Applications, 1A (2), 165–172, (2000).

18) Elliptic boundary value problem in vanishing mean oscillation hypothesis, Commentationes Mathematicae Universitatis Carolinae, 40, (4), 651–663, (1999).7

19) C (0,α)−regularity of the solution of the Dirichlet problem for elliptic equations in divergence form, Int. Journal of Differential Equations and Applications, 1 (1), 113–125, (2000).

20) Regular oblique derivative problem in Morrey spaces (in coll. D.K. Palagachev, L. Softova), Electr. Journal of Differential Equations, n.39,1–17, (2000)

http://www.emis.de/journals/EJDE/Volumes/2000/39.

21) Regularity theory associated to operators with non euclidean geometry, International Journal of Differential Equations and Applications, 3 (4), 459–466, (2001).

22) A potential theoretic inequality (in coll. P. Zamboni), Czechoslovak Mathematical Journal, 51 (126), 55–65, (2001).

23) H¨older regularity for solutions of ultraparabolic equations in divergence form, (in coll. S. Polidoro), Potential Analysis, 14, 341–350, (2001).

24) Stime interne per equazioni ultraparaboliche in forma di divergenza, Proceedings of XVI Congresso U.M.I., (1999).

25) On weak solutions of ultraparabolic equations, Nonlinear Analysis, 47, 503–511, (2001).

26) Boundary value problems for uniformly elliptic operators, Applicable Mathematics, Its Perspectives and Challenges, 82–87 (2001).

27) Istituzioni di Analisi Superiore, (book in coll. G. Santagati), ed. Spazio Libri (2001).

28) A Green function and regularity results for an ultraparabolic equation with a singular potential (in coll. S. Polidoro), Advances in Differential Equations, 7 (2002), 1281–1314, (2002).

29) Local h¨older regularity for solutions of elliptic system, Duke Mathematical Journal, 113 (2) (2002).

30) Parabolic systems with non continuous coefficients, Discrete and Continuous Dynamical Systems, 727–733, (2002).

31) Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients (in coll. D.K. Palagachev, L. Softova), Bollettino Unione Matematica Italiana (8) 6-B, 667–683, (2003).

32) Alcuni contributi allo studio di equazioni paraboliche di tipo variazionale, Proceedings of XVII Congresso U.M.I. (2003).

33) Interior estimates in Campanato spaces related to quadratic functionals (in coll. A. Tachikawa), Proceedings of Research Institute of Mathematical Sciences, Kyoto, 54–65 (2004).

34) Cauchy-Dirichlet problem associated to divergence form parabolic equations, Communications in Contemporary Mathematics, 6 (3), 377–393, (2004).

35) Quasilinear equations with discontinuous coefficients, Communications in Applied Analysis, 9, 337–341 (2005).

36) H¨older regularity results for solutions of parabolic equations, Journal of Global Optimization, 79 (2005) 921–934, (2005).

37) Partial regularity of the minimizers for quadratic functionals with VMO coefficients (in coll. A. Tachikawa), London Mathematical Society,72 (3), 609–620 (2005).8

38) The Cauchy-Dirichlet problem for parabolic equations with VMO coefficients, Mathematical and Computer Modelling, 42, 1245–1254 (2005).

39) On continuity of minimizers for certain quadratic growth functionals (in coll. A. Tachikawa), Journal of Mathematical Society of Japan, 57

(3), 691–700, (2005).

40) On some Schr¨odinger type equations, Proceedings of the 5th ISAAC Congress, World Scientific, 729–736, (2005).

41) Trends and topics on some partial differential equations and systems, Le Matematiche 60 (II), 447–456 (2005).

42) On sets of zero Hausdorff s-dimensional measure, Proceedings of the Conference on Differential and Difference Equations and Applications, Hindawi Publishing Corporation, 963–968 (2006).

43) Continuity of the derivatives of solutions related to elliptic equations, Proceedings of the Royal Society of Edinburgh, 136 (A), 1027–1039 (2006).

44) Solvability of a Dirichlet problem for divergence form parabolic equations, Journal of Nonlinear and Convex Analysis, 7 (3), 515–524 (2006).

45) On certain regularity properties, Bollettino della Accademia Gioenia, 39 (366), 201–206 (2008).

46) On positive solutions of hypoelliptic second order differential equations, Lecture Notes of Seminario Interdisciplinare di Matematica,6, 209–216 (2007).

47) Linear growth coefficients in quasilinear equations, Nonlinear Differential Equations and Applications, 13, 605–6 (2007)17.

48) Su una classe di problemi ellittici non lineari, Proceedings of XVIII Congresso U.M.I. (2007).

49) Commutators of fractional integral operators in Vanishing-Morrey Spaces, Journal of Global Optimization, 40 (1), 361–368 (2008).

50) Regularity of the minimizers of some variational integrals (in coll. with A. Tachikawa), Zeitschrift f¨ur Analysis und ihre Anwendungen, 27 (4) , 469-482 (2008).

51) Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term (in coll. S. Polidoro) Revista Mathematica Iberoamericana, 24 (3), 1011–1046 (2008).

52) Homogeneous Herz spaces and regularity results, Nonlinear Analysis Series A: Theory, Methods and Applications 71, 1–6 (2009).

53) Recent advances in Homogeneous Herz spaces and PDE’s, American Institute of Physics Inc., T. Simos, G. Psihoyios; Ch. Tsitouras; (Eds.), 2 1492–1495, (2009).

54)On a class of derivatives of some vector-valued minimizers, CIRO’10 The Fifth International Conference on Operations Research, Marrakech, (2010).

55) Estimates of the derivatives of minimizers of a special class of variational integral (in coll. A. Tachikawa), Discrete and Continuous Dynamical Systems, 31 (3), 1411–1425 (2011).9

56) A new regularity criterion for the nematic liquid crystal flows, (incoll. S. Gala, Q. Liu), Applicable Analysis 1–7 (2011).

57) Immune system network and cancer vaccine (in coll. C. Bianca, M. Pennisi, S. Motta), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, T. Simos, G. Psihoyios; Ch. Tsitouras Eds., (2011).

58) Metodi e modelli matematici (book in coll. S. Motta), ed. Culc (2011).

59) Metodi e modelli matematici- Esercizi e Complementi (book in coll.S. Motta, A. Scapellato), ed. Culc (2013).

60) Interpolation inequalities for weak solutions nonlinear parabolic systems (in coll. G. Floridia), Journal of Inequalities and Applications 42, doi:10.1186/1029-242X-2011-42, (2011).

61) Differentiability and partial Holder continuity of solutions of nonlinear elliptic systems (in coll. G. Floridia), Journal of Convex Analysis I (19) (2012).

62) Regolarit´a per i flussi di cristalli liquidi nematici, (in coll. S. Gala, Q. Liu) pubblicata negli Atti del XIX Congresso U.M.I. (2011).

63) Parabolic Herz spaces and their applications, Applied Mathematical Letters, 25 (10), 1270–1273 (2012).

64) Embeddings for Morrey-Lorentz Spaces, Journal of Optimization Theory and Applications, 154 (2), 491–499 (2012).

65) Necessary and Sufficient condition for a V MO function, Appl. Math. Computation, 218 (24) 11952–11958 (2012).

66) On some results in weighted Morrey spaces with applications to PDE Dept. of engineering sciences and mathematics, research report 2012-02 (in coll. L.-E. Persson, N. Samko, P. Wall), ISSN:1400-4003 (2012).

67) Partial regularity for p(x)−harmonic maps (in coll. A. Tachikawa, H. Takabayashi), Transaction of the American Mathematical Society,365, 3329–3353 (2013).

68) Uniqueness criterion of weak solutions for the dissipative quasigeostrophic equations in Orlicz-Morrey spaces (in coll. S. Gala, Y. Sawano, H. Tanaka), Applicable Analysis, 1–7, doi:10.1080/00036811.2013.772582 (2013).

69) Logarithmically improved regularity criterion for the nematic liquid crystal flows in B˙ −1 ∞,∞ (in coll. S. Gala, Q. Liu), Computers and Mathematics with Applications, 65 (2013), 1738–1745.

70) On the regularity criteria for the 3D magnetohydrodynamic equations via two components in terms of BMO space (in coll. S. Gala), Mathematical Methods in the applied Sciences, 37 (15), 2320–2325 (2013).

71) Remarks on Leray’s self-similar solutions to the 3D MHD equations (in coll. S. Benbernou, M. Terbeche), Mathematical Methods in the Applied Sciences, 37 (17) 2615–2618 (2014).

72) A remark on regularity criterion of the Boussinesq equations with zero heat conductivity (in coll. S. Gala, Z. Guo), Applied Mathematical Letters, 27, 70–73 (2013). 10

73) On the regularity criteria for the 3D magnetohydrodynamic equations via two components in terms of BMO space (in coll. S. Benbernou, S. Gala), Mathematical Methods in the Applied Sciences, 37 (15), 2320–2325 (2013).

74) Persistence Analysis in a Kolmogorov-type Model for Cancer - Immune System Competition (in coll. C. Bianca, F. Pappalardo, M. Pennisi),Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, 1558, 1797–1800 (2013).

75) On interior regularity of minimizers of p(x)-energy functionals (in coll. A. Tachikawa), Nonlinear Analysis, 93 162-167 (2013).

76) New enviromentally sensitive patch index – ESPI– for MEDALUS protocol, (in coll. A. Duro, V. Piccione, V. Veneziano), AIP Conf. Proc., 10th Int. Conf. on Math. Problems in Engineering, Aerospace and Sciences, ICNPAA 1637, 305-312 (2014).

77) The enviromentally sensitive patch applied to Medalus climate quality index, (in coll. A. Duro, V. Piccione, V. Veneziano), AIP Conf. Proc., CNAAM 1738, 480113 (2016).

78) A regularity criterion in terms of pressure for the 3D viscous MHD equations, (in coll. S. Gala, Z.Zhang), Bull, of the Malaysian Math. Soc., ISSN:0126-6705, 40 (4), 1677-1690 (2015), doi:10.1007/s40840-015-0160-y,

79) A regularity criterion for the three-dimensional MHD equations in terms of one directional derivative of the pressure , (in coll. S. Gala, Z.Guo), Computers and Mathematics with Applications 70 (12), 3057-3061 (2015).

80) A regularity criterion for 3D micropolar fluid flows in terms of one partial derivative of the velocity, (in coll. S. Gala), Annales Polonici Mathematici 116 (3), 217-228 (2016).

81) A new regularity criterion for the Navier-Stokes equations in terms of the two components of the velocity, (in coll. S. Gala), El. Journal of Qualitative Theory of Differential Equations, 26, 1-9 doi:10.14232/ejqtde.2016.1.XX (2016).

82) A new regularity criterion for strong solutions to the Ericksen–Leslie system, (in coll. S. Gala), Applicationes Mathematicae 43 (1), 95–103 (2016).

83) Boundary regularity of minimizers of p(x)-energy functionals (in coll.A. Tachikawa), Annales de l’Institut Henri Poincare / Analyse non lineaire, 33 (2) (2016) 451-476, doi:10.1016/j.anihpc.2014.11.003 (2016).

84) Logarithmically improved regularity criteria for supercritical quasigeostrophic equations in Orlicz-Morrey Spaces, (in coll. S. Gala), Electronic Journal of Differential Equations, 2016, 1–7 (2016).

85) A logarithmic regularity criterion for the two-dimensional MHD equations, (in coll. S. Gala), Journal of Mathematical Analysis and Applications, 444 (2), 1752–1758 (2016).

86) Note on the weak-strong uniqueness criterion for the β-QG in Morrey - Campanato space, (in coll. S. Gala), Applied Mathematics and Computation, 293, 65–71 (2017).11

87) On the blow-up criterion of strong solutions for the MHD equations with the Hall and ion-slip effects in R3, (in coll. S. Gala), Zeitschrift fur Angewandte Mathematik und Physik, 67 (2) art.n. 18 (2016).

88)A Remark on the Beale-Kato-Majda Criterion for the 3D MHD Equations with Zero Magnetic Diffusivity, (in coll. S. Gala) AIP Conference Proceedings, 1738 art.n. UNSP 480115 (2016).

89) Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices, (in coll. S. Gala)Applicable Analysis, 95 (6) 1271-1279, (2016).

90)Logarithmical regularity criterion of the three-dimensional Boussinesq equations in terms of the pressure, (in coll. M. Mechdene, S. Gala, Sadek, Z. Guo) , Zeitschrift fur Angewandte Mathematik und Physik, 67 (5) art.n. 120 (2016).

91) Enviromentally Sensitive Path Index of desertification risk in the main habitat of Sicily (in coll. A. Duro, V. Piccione, V. Rapicavoli, V. Veneziano), AIP Conf. Proc., ICNAAM 1863, art.n.UNSP 510005,(2017).

92)On the regularity in some variational problems (in coll. A.Tachikawa), AIP Conf. Proc., 11th Int. Conf. on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA, 1798, doi:10.1063/1.4972720 (2017).

93) Study of saharian dust influence of PM10 measures in Sicily from 2013 to 2015 (in coll. A. Cuspilici, P. Monforte), Ecological Indicators 76, 297-303 (2017).

94) Note on the blow-up criterion for generalized MHD equations (incoll. S. Gala), AIP Conf. Proc., 11th Int. Conf. on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA, 1798, doi: 10.1063/1.4972650 (2017).

95) Intrinsic Square Functions on Vanishing Generalized Orlicz-Morrey Spaces, (in coll. V. Guliyev, F. Deringoz), Set-Valued Analysis and Applications, 25 (4), 807-828 (2017).

96) Mixed Morrey Spaces and their applications to partial differential equations , (in coll. A. Scapellato), Nonlinear Analysis, Theory, Methods and Applications, 151, 51–65 (2017).

97) An improved blow-up criterion for smooth solutions of the twodimensional MHD equations, (in coll. S. Gala, Z. Ye), Mathematical Methods in the Applied Sciences, 40 (1) 279–285 (2017).

98) Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth, (in coll. F. Giannetti, A. Passarelli di Napoli, A. Tachikawa), Calculus of Variations and Partial Differential Equations, 56 (6), (2017).

99) On minimizers for functionals under the non-standard growth conditions, (in coll. A. Tachikawa), AIP Conference Proceedings 1738,480112 (2016).

100)Levels of desertification risk in the sicilian forests according to MEDALUS -ESPI protocol (in coll. V. Rapicavoli), AIP Conf. Proc., ICNAAM 1863 art.n. 530004 (2017).12

101) A logarithmically improved regularity criterion for the 3D MHD equations in Morrey-Campanato space, (in coll. S. Gala),AIMS Mathematics, 2 (1) 16-23 (2017).

102)A logarithmically improved regularity criterion for the MHD equations in terms of one directional derivative of the pressure, (in coll. S. Benbernou, M. Terbeche), Applicable Analysis, 96 (12) 2140-2148, (2017).

103) A regularity criterion of weak solutions to the 3D Boussinesq equations, (in coll. A.M. Alghamdi, S. Gala), AIMS Mathematics, 2 (3) 451–457 doi: 10.3934/Math.2017.2.451 (2017).

104) On the regularity criterion for the Navier-Stokes equations in terms of one directional derivative, (in coll. S. Gala), Asian-European Journal of Mathematics, 10 (1) art. n.1750012 (2017).

105) A note on regularity criteria in terms of pressure for the 3D viscous MHD equations, (in coll. S. Gala), Mathematical Notes, 102 (3-4) 475–479 (2017).

106) Logarithmically improved regularity criteria for the Boussinesq equations, (in coll. S. Gala, M. Mechdene), AIMS Mathematics, 2 (2) 336-347 (2017).

107) New challenges on the regularity of minimizers of functionals, (incoll. A. Tachikawa), Journal of Convex Analysis, 25 (2), 675–690 (2018).

108) On the Blow-Up Criterion for Incompressible Stokes-MHD Equations, (in coll. con A.M. Alghamdi, S. Gala), Results in Mathematics, 73(3) Article Number: UNSP 110 (2018).

109) Naturalit´a e vulnerabilit´a nei Siti Natura 2000 che insistono suicorridoi ecologici del versante jonico calabrese. Caso sudio SIC Foce Neto, (incoll. C. Arcidiacono, R.M.S. Costa, I. Grasso, V. Rapicavoli, M. Seminara,V. Veneziano), Boll. Accademia Gioenia di Scienze Naturali, 51(381), 7–145, ISSN: 0393-7143 (2018).

110) Commutators and Generalized Local Morrey Spaces, (in coll. V.Guliyev, M. Omarova, A. Scapellato), Journal of Mathematical Analysis and Applications, 457 (2), 1388–1402 (2018).

111) New regularity criteria for the 3D Hall-MHD equations, (in coll.A.M. Alghamdi, S. Gala), Annales Polonici Mathematici, 121 (1) 7–20(2018).

112) Weighted extrapolation in grand Morrey spaces and applications to partial differential equations, (in coll. Vakhtang Kokilashvili, Alexander Meskhi) Rend. Lincei Mat. Appl, 30 (2019), doi: 10.4171/RLM/836,67-92.

113) Evaluation of the air pollution in a Mediterranean region by the air quality index (in coll. P. Monforte), Environ. Monit. Assess. 190:625, doi: 10.1007/s10661-018-7006-7, (2018).

114) Regularity for minimizers for functionals of double phase with variable exponents, (in coll. A. Tachikawa), Advances in Nonlinear Analysis, (2019).

115) Identification of enduring Saharan dust storms in a Mediterranean island: Day 1 by day analysis of the contribution given on the PM10 measurements, (in coll. P. Monforte), preprint.13

116)Moser’s estimates for degenerate Kolmogorov equations with nonnegative divergence lower order coefficients, (in coll. F. Anceschi, S. Polidoro), reprint.

117)Partial regularity of minimizers of asymptotically convex functionals with p(x)-growth, (in coll. C. Goodrich, A. Scapellato), preprint.

118)H¨older continuity of weak solutions of p-Laplacian PDEs with VMO coefficients, (in coll. C. Goodrich), Nonlinear Analysis, (2019).

119)Partial regularity of solutions to p(x)-Laplacian PDEs with discontinuous coefficients, (in coll. C. Goodrich, A. Scapellato), preprint.120) Sequence of solutions for some nonlocal elliptic problem in RN . (incoll. con M. Makvand Chaharlang, A. Razani), preprint.