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.
Bianchini, C., Ciraolo, G. (2018). Wulff shape characterizations in overdetermined anisotropic elliptic problems. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 43(5), 790-820 [10.1080/03605302.2018.1475488].
Wulff shape characterizations in overdetermined anisotropic elliptic problems
Ciraolo, G.
2018-01-01
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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