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W2951667076 abstract "In this paper we discuss the obstacle problem for the $p$-Laplace operator. We prove optimal growth results for the solution. Of particular interest is the point-wise regularity of the solution at free boundary points. The most surprising result we prove is the one for the $p$-obstacle problem: Find the smallest $u$ such that $$ hbox{div} (|nabla u|^{p-2}nabla u) leq 0, qquad ugeq phi, qquad hbox{in } B_1, $$ with $phi in C^{1,1}(B_1)$ and given boundary datum on $partial B_1$. We prove that the solution is uniformly $C^{1,1}$ at free boundary points. Similar results are obtained in the case of an inhomogeneity belonging to $L^infty$. When applied to the corresponding parabolic problem, these results imply that any solution which is Lipschitz in time is $C^{1,frac{1}{p-1}}$ in the spatial variables." @default.
W2951667076 created "2019-06-27" @default.
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W2951667076 date "2014-02-20" @default.
W2951667076 modified "2023-10-01" @default.
W2951667076 title "Optimal regularity for the obstacle problem for the $p$-Laplacian" @default.
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