The Singular Set of Higher Dimensional Unstable Obstacle Type Problems

2012/07/14 by Andersson, John, Shahgholian, Henrik, Weiss, Georg
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.3398

Abstract

In this paper we will investigate the singular points of the following unstable free boundary problem: equation Δu= -χ_\u>0\ \textrmin B₁(0) equation where χ_\u>0\ is the characteristic function of the set \u>0\.

Related

• The fractional unstable obstacle problem
• The structure of the regular part of the free boundary close to singularities in the obstacle problem
• On the fine regularity of the singular set in the nonlinear obstacle problem
• On the fine structure of the free boundary for the classical obstacle\n problem
• Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian