Analysis of a free boundary at contact points with Lipschitz data

Aram Karakhanyan, Henrik Shahgholian

In this paper we consider a minimization problem for the functional $$ J(u)=\int_{B_1^+}|\nabla u|\sp 2+λ_{+}^2χ_{\{u>0\}}+λ_{-}^2χ_{\{u\leq0\}}, $$ in the upper half ball $B_1^+\s…