The two membranes problem in a regular tree

Abstract

In this paper we study the two membranes problem for operators given in terms of a mean value formula on a regular tree. We show existence of solutions under adequate conditions on the boundary data and the involved source terms. We also show that, when the boundary data are strictly separated, the coincidence set is separated from the boundary and thus it contains only a finite number of nodes.

References in corpus (6)

• Tug-of-war and the infinity Laplacian
• Geometric analysis on Cantor sets and trees
• The unique continuation property for a nonlinear equation on trees
• Estimates for Nonlinear Harmonic Measures on Trees
• Existence, uniqueness and decay rates for evolution equations on trees
• Dirichlet-to-Neumann maps on Trees