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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Shigeru Sakaguchi
Journal: Proc. Amer. Math. Soc. 95 (1985), 382-386
MSC: Primary 35R35; Secondary 31C99, 49A29
MathSciNet review: 806075
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Abstract: We consider the obstacle problem for the $ p$-harmonic operator

$\displaystyle {\text{div}}\left( {{{\left\vert {\nabla \cdot } \right\vert}^{p - 2}}\nabla \cdot } \right)\quad {\text{with}}\;p > 1,$

and show that the coincidence set is star shaped under certain conditions on the obstacle.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806075-1
PII: S 0002-9939(1985)0806075-1
Article copyright: © Copyright 1985 American Mathematical Society