Wulff shape characterizations in overdetermined anisotropic elliptic problems

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.

References in corpus (3)

• Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations
• Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs
• A rigidity problem on the round sphere

Cited by in corpus (1)

• Radial symmetry for p-harmonic functions in exterior and punctured domains