PDEs and Applications seminar: Anisotropic elliptic problems

  • Date: –11:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Iwona Chlebicka, University of Warsaw
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

Abstract: Let us consider a nonlinear elliptic Dirichlet problem with nonstandard growth expressed by the means of fully anisotropic Orlicz function on which no condition of doubling type is imposed. This type of equations are related to elasticity problems of materials of complicated structure or steady flow of non-Newtonian fluids. I shall concentrate on explanation what this anisotropy means, what type of operators are included in the study and, consequently, what is the meaning of the equation we study. When the datum is regular, we prove existence of weak solutions. For measure data we consider a generalized notion of solutions for which we infer existence and anisotropic regularity in Orlicz-Marcinkiewicz spaces extending the known results for anisotropic p-Laplace equation. In the case of datum absolutely continuous with respect to Lebesgue's measure we prove also uniqueness. Based on joint work: with Angela Alberico, Andrea Cianchi and Anna Zatorska-Goldstein, Fully anisotropic elliptic problems with minimally integrable data Calc. Var. PDEs (2019) 58:186.