Gradient Estimates for weak solutions of Elliptic PDE's - Seminar

Seminar
Event Start
Event End
Location
Building 1, Level 4, Room 4214
Giuseppe Di Fazio, Professor, Mathematics and Computer Sciences, University of Catania, Italy

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)