[Plenary Lecture] Potential Analysis on Nonsmooth Domains

Speaker: Professor Hiroaki Aikawa, Chubu University

Title: Potential Analysis on Nonsmooth Domains

Abstract: The Laplace and heat equations are classical and often considered well understood. However, many questions about the boundary behavior of solutions and supersolutions in general domains remain open. In this talk, we explore how domain complexity affects potential-theoretic properties, including the integrability of positive superharmonic functions, the Martin boundary, elliptic and parabolic boundary Harnack principles, intrinsic ultracontractivity, and related notions. To this end, we examine various nonsmooth domains, such as Lipschitz, NTA, uniform, inner uniform, John, Hölder, and \(L^p\) domains, among others. The first lecture presents the main results, while the second provides an outline of the key techniques and proof strategies.