We consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone Σ intersected with the exterior of a bounded domain Ω in RN, N≥ 2. Under a prescribed logarithmic condition at infinity, we prove a rigidity result by showing that the existence of a solution implies that Σ ∩ Ω must be the intersection of the Wulff shape and Σ. Our approach is based on a Pohozaev-type identity and the characterization of minimizers of the anisotropic isoperimetric inequality inside convex cones.

An exterior overdetermined problem for Finsler N-Laplacian in convex cones / G. Ciraolo, X. Li. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 61:4(2022 May 05), pp. 121.1-121.27. [10.1007/s00526-022-02235-2]

An exterior overdetermined problem for Finsler N-Laplacian in convex cones

G. Ciraolo
Primo
;
2022

Abstract

We consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone Σ intersected with the exterior of a bounded domain Ω in RN, N≥ 2. Under a prescribed logarithmic condition at infinity, we prove a rigidity result by showing that the existence of a solution implies that Σ ∩ Ω must be the intersection of the Wulff shape and Σ. Our approach is based on a Pohozaev-type identity and the characterization of minimizers of the anisotropic isoperimetric inequality inside convex cones.
Settore MAT/05 - Analisi Matematica
5-mag-2022
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/939497
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