Research Seminar in Mathematics - Degenerate Kolmogorov-type equations with rough coefficients - Potential theory and boundary regularity

Speaker

Malte Litsgård, Uppsala University

Abstract

Today Kolmogorov-type operators with low-regularity coefficients have applications in many different areas: analysis, physics, and finance, to name a few. In particular the study of local regularity of weak solutions to PDEs associated to such operators is relevant in for example kinetic theory, where these equations appear in relation to the study of conditional regularity of the Boltzmann and Landau equations. In this talk I will give some background for these operators and present some results concerning potential theory and boundary regularity in Lipschitz-type domains.