Stability remarks to the obstacle problem for p-Laplacian type equations

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, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1\! < \!p\! < \!\infty$\end{document}. We rely on the local \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C^{1,\lambda}$\end{document} 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.