Tomasz Adamowicz: p-Laplace type equations of nonstandard growth
Tomasz Adamowicz, Linköping university
Time: Wed 2013-02-20 10.30 - 11.30
Location: Room 306, building 6, Kräftriket, Department of Mathematics, Stockholm University
The purpose of the talk is to discuss the fundamental object of nonlinear potential theory, the so-called p-harmonic operator and related p(x)-harmonic type equation, also known as variable exponent p-Laplacian. We explain the basic properties of the p(x)-Laplacian and show the unexpected and fruitful interplay between PDEs and quasiregular mappings. We also present Harnack inequality and the global integrability of supersolutions for p(x)-Laplacian.
If time permits we discuss the boundary regularity for p(x)-Laplacian. Among others, we introduce regular and irregular boundary points and explain the Kellogg property and trichotomy result.
The presentation is based on join projects with Peter Hästö from Oulu University and Anders and Jana Björn from Linköping University.