The free boundary of variational inequalities with gradient constraints

Abstract

In this paper we prove that the free boundary of some variational inequalities with gradient constraints is as regular as the tangent bundle of the boundary of the domain. To this end, we study a generalized notion of ridge of a domain in the plane, which is the set of singularities of the distance function in the p-norm to the boundary of the domain.

arXiv commentCompared to the published version, here we added several explanatory footnotes to make the article more perspicuous. 23 pages