Quasi-linear PDEs and low-dimensional sets

Abstract

In this paper we establish new results concerning boundary Harnack inequalities and the Martin boundary problem, for non-negative solutions to equations of p -Laplace type with variable coefficients. The key novelty is that we consider solutions which vanish only on a low-dimensional set \Sigma in \mathbb R^n and this is different compared to the more traditional setting of boundary value problems set in the geometrical situation of a bounded domain in \mathbb R^n having a boundary with (Hausdorff) dimension in the range [n-1,n) . We establish our quantitative and scale-invariant estimates in the context of low-dimensional Reifenberg flat sets.

Locations

• KTH Publication Database DiVA (KTH Royal Institute of Technology) - View - PDF
• Journal of the European Mathematical Society - View