The 10th International Conference on Fuzzy Systems and Data Mining (FSDM 2024)

Abstract: Let us consider an elliptic equation of second order in variational form in a bounded domain of the Euclidean n dimensional space. The right hand side is a function satisfying suitable assumptions. The problem of gradient estimates for elliptic equations is very important both from theoretical and applied point of view. In this talk we exploit what is the heart of the technique to show gradient estimates allowing the function f to belong to very general function spaces. Our technique is very flexible and it is allowed to show existence, uniqueness and well posedness of the Dirichlet problem in several classes.

Biography: Born in Catania in 1963, with a degree in Mathematics (University of Catania) in 1986 110/110 cum laude, PhD in 1992 in Mathematics - Partial Differential Equations under the supervision of Professor Filippo Chiarenza, University of Catania, Dr. Giuseppe Di Fazio has been a Full Professor since 2007 at University of Catania. He is also Visiting Professor at University of Bologna, University of Firenze, Politecnico di Milano, Università di Napoli, Università di Salerno, Università di Urbino, Università di Trento, Temple University (Philadelphia PA), MSRI (Berkeley CA), Università Autonoma de Madrid, Tokyo Metropolitan University, Tokyo University of Sciences, Chuo University in Tokyo, University of Kyoto, Bandung Institute of Technology.
His research interests are about regularity problems for elliptic PDEs and boundedness properties of integral operators acting on Morrey spaces.
Author of the books
1. Yoshihiro Sawano - Giuseppe Di Fazio - Denny Ivanal Hakim - Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s, Volume I ISBN:9781498765510 - Taylor & Francis (2020)
2. Yoshihiro Sawano - Giuseppe Di Fazio - Denny Ivanal Hakim - Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s, Volume II ISBN: 9780367459154 – Taylor & Francis (2020)