Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 61, Issue 4, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-022-02235-2
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Funding
- Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM, Italy)
- China Scholarship Council
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In this paper, the authors consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone. They prove the existence of a solution and a rigidity result using a prescribed logarithmic condition and the characterization of minimizers of anisotropic isoperimetric inequality inside convex cones.
We consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone Sigma intersected with the exterior of a bounded domain Omega in R-N, N >= 2. Under a prescribed logarithmic condition at infinity, we prove a rigidity result by showing that the existence of a solution implies that Sigma boolean AND Omega must be the intersection of the Wulff shape and Sigma. Our approach is based on a Pohozaev-type identity and the characterization of minimizers of the anisotropic isoperimetric inequality inside convex cones.
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