Abstract
We extend some convergence and L1 stability results for the coincidence set to the p-obstacle problem under natural nondegeneracy conditions and without restrictions on p, \(1\! < \!p\! < \!\infty\). We rely on the local \(C^{1,\lambda}\) regularity of the solution and, as an application, we show the existence of a solution to the thermal membrane problem, and in a limit nonlocal case also its uniqueness for small data.
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