Gradient Estimates for weak solutions of Elliptic PDE's - Seminar
- Giuseppe Di Fazio, Professor, Mathematics and Computer Sciences, University of Catania, Italy
B1 L4 R4214
Let us consider an elliptic equation of second order in variational form i.e. div(A(x)∇u) = divf in a bounded domain Ω ⊂ Rn where the function f belongs to some suitable function space.
Overview
Abstract
Let us consider an elliptic equation of second order in variational form i.e.
div(A(x)∇u) = divf
in a bounded domain Ω ⊂ Rn where the function f belongs to some suitable function space. The gradient estimates problem is very important both from a theoretical and applied point of view. In the Seminar 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 allows to show the existence, uniqueness, and well-posedness of the Dirichlet problem in several classes. As an example, we will give the result in W01,p.
Brief Biography
- Born in Catania in 1963. 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.
- Assistant Professor from 1992, Associate Professor from 1998, and Full Professor from 2007 at the University of Catania.
- Chair of Master program in Mathematics at the University of Catania.
- Visiting Professor in Italy at the University of Bologna, University of Firenze, Politecnico di Milano, Universit`a di Napoli, Universit`a di Salerno, Universit`a di Urbino, Universit`a di Trento.
- Visiting Professor at Temple University (Philadelphia PA), MSRI (Berkeley CA), Universit`a Autonoma de Madrid, Tokyo Metropolitan University, Tokyo University of Sciences, Chuo University in Tokyo, University of Kyoto, KAUST (Saudi Arabia), Bandung Institute of Technology ITB (Indonesia), University of Coimbra (Portugal).
- Research interests are about regularity problems for elliptic PDEs and boundedness properties of integral operators acting on Morrey spaces.
- Author of the books:
- 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)
- 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)