Title:  Operators of p Laplace Type: Estimates for Solutions Vanishing on Lower Dimensional Sets

Abstract:  In this talk I will first review work with Kaj Nystr¨om concerning boundary Harnack in- equalities, the Martin boundary problem, and boundary regularity for non-negative solutions to equations of p-Laplace type in domains whose boundaries are Lipschitz or sufficiently flat in the sense of Reifenberg. After that I will discuss work in progress with Nystr¨om concerning boundary Harnack inequalities, the Martin boundary problem, and boundary regularity for non-negative solutions to equations of p- Laplace type vanishing on codimension > 1 Reifenberg flat sets in Euclidean n space for certain values of p. The novelty of our work is that more traditional boundary value problems (eg, boundary value problems for the Laplace operator) require that the boundary have a certain fatness in order that a solution exist.