We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.
Wulff shape characterizations in overdetermined anisotropic elliptic problems / C. Bianchini, G. Ciraolo. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 43:5(2018), pp. 790-820. [10.1080/03605302.2018.1475488]
Wulff shape characterizations in overdetermined anisotropic elliptic problems
G. Ciraolo
2018
Abstract
We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.
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