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

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Location
Building 1, Level 4, Room 4214

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)

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