Coincidence sets in the obstacle problem for the 𝑝-harmonic operator

Sakaguchi, Shigeru

doi:10.1090/S0002-9939-1985-0806075-1

Coincidence sets in the obstacle problem for the $p$-harmonic operator
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Proc. Amer. Math. Soc. 95 (1985), 382-386 Request permission

Abstract:

We consider the obstacle problem for the $p$-harmonic operator \[ {\text {div}}\left ( {{{\left | {\nabla \cdot } \right |}^{p - 2}}\nabla \cdot } \right )\quad {\text {with}}\;p > 1,\] and show that the coincidence set is star shaped under certain conditions on the obstacle.

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