An overdetermined p-Laplace problem forces the domain to be a half-space or to have strictly negative boundary mean curvature, under a condition on the nonlinearity.
Modica-type estimates and curvature results for overdetermined elliptic problems
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Modica type estimates and curvature results for overdetermined $p$-Laplace problems
An overdetermined p-Laplace problem forces the domain to be a half-space or to have strictly negative boundary mean curvature, under a condition on the nonlinearity.