Overdetermined problems for the normalized 𝑝-Laplacian

Banerjee, Agnid; Kawohl, Bernd

doi:10.1090/bproc/33

Overdetermined problems for the normalized $p$-Laplacian
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by Agnid Banerjee and Bernd Kawohl HTML | PDF

Proc. Amer. Math. Soc. Ser. B 5 (2018), 18-24

Abstract:

We extend the symmetry result of Serrin \cite{S} and Weinberger \cite{W} from the Laplacian operator to the highly degenerate game-theoretic $p$-Laplacian operator and show that viscosity solutions of $-\Delta _p^Nu=1$ in $\Omega$, $u=0$ and $\tfrac {\partial u}{\partial \nu }=-c\neq 0$ on $\partial \Omega$ can only exist on a bounded domain $\Omega$ if $\Omega$ is a ball.

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