Research group about Elliptic PDEs under minimal assumptions

Books

  • Y. Sawano, G. Di Fazio, D.I. Hakim - Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s, Volume I ISBN:9781498765510
  • Y. Sawano, G. Di Fazio, D.I. Hakim - Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s, Volume II ISBN:9780367459154
  • G. Di Fazio, Maria Stella Fanciullo, Pietro Zamboni - Special Issue on Current Trends in Elliptic and Parabolic Problems. Le Matematiche 75 n.1 (2020) (Editors)

Recent Papers

  • G. Di Fazio, M. S. Fanciullo, A. Morassi, P. Zamboni, Bounded deformation for a spider orb web, SIAM, Journal on Mathematical Analysis 58, issue 2 (2026).

  • G. Di Fazio, M. S. Fanciullo, S. Rodney, P. Zamboni, Harnack inequality for degenerate elliptic equations with matrix weights, Advances in Calculus of Variations (2025); 18(4): 1327-1338.

  • G. Di Fazio, R.Teymurazyan, J.M.Urbano, Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces. Annali di Matematica 205, 929–940 (2026). https://doi.org/10.1007/s10231-025-01628-2

  • A. M. Alharbi, G. Di Fazio, D.A. Gomes, M. Ucer Regularity for Weak Solutions to First-Order Local Mean Field Games NoDeA (2025) - DOI: https://doi.org/10.1007/s00030-025-01099-7 Nonlinear Differ. Equ. Appl. (2025) 32:99

  • G. Di Fazio Y. Miyazaki; Sobolev-Morrey spaces via Muramatu's integral formula - Analysis and Applications ISSN (print): 0219-5305 | ISSN (online): 1793-6861 - DOI: 10.1142/S0219530525300017 - Vol. 24, No. 3, pp. 591-614

  • G. Di Fazio, F. Mamedov, - On Harnack inequality and Hoelder continuity for non uniformly elliptic equations Ricerche di Matematica (2024) https://doi.org/10.1007/s11587-024-00919-9.

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni - Smoothness for Degenerate Elliptic Equations with Matrix Weights. Chapter in the book Analysis and Applied Mathematics - ISBN: 978-3-031-62667-8, Springer BWF: 605718 (2024) pp. 163-169

  • T. Bakaryan, G. Di Fazio, D. Gomes - C^{1,\alpha} Regularity For Stationary Mean-Field Games With Logarithmic Coupling - Non linear Differential Equations and applications NoDEA, (2024)

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni, S. Rodney, D. Monticelli - Matrix weights and regularity for degenerate elliptic equations - Nonlinear Analysis 237, December 2023, 113363.

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni - Boundary regularity for strongly degenerate operators of Grushin type, Electron. J. Differential Equations, 2022 (2022), No. 65, pp. 1-16.

  • G. Di Fazio, L. Aharouch, M. Kbiri Alaoui, M. Altanji - On a class of nonlinear elliptic problems with obstacle. Georgian Math. J. 28 (2021), no. 5, 665–675. DOI: https://doi.org/10.1515/gmj-2020-2085

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni - Nonlinear elliptic equations related to weighted sum operators. DOI: 10.1016/j.na.2019.07.003 Nonlinear Analysis 194 May (2020)

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni - Boundary Harnack type inequality and regularity for quasilinear degenerate elliptic equations. Harnack inequalities and nonlinear operators, 139–157, Springer INdAM Ser., 46

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni - Local regularity for strongly degenerate elliptic equations and weighted sum operators Journal of Differential and Integral Equations 32, N 7-8, July/August (2019)

  • G. Di Fazio, M.S. Fanciullo, P. Zamboni - Harnack inequality and smoothness for some non linear degenerate elliptic equations - Minimax Theory and its Applications 4 (2019)

  • G. Di Fazio, T. Nguyen - Gradient estimates for quasilinear elliptic equations in weighted Morrey spaces - Revista Matematica Ibero Americana (2019)