We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in RN, establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of Reichel (Arch Ration Mech Anal 137(4):381–394, 1997), where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm H. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm H0).

Bianchini, C., Ciraolo, G., & Salani, P. (2016). An overdetermined problem for the anisotropic capacity. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 55(4) [10.1007/s00526-016-1011-x].

An overdetermined problem for the anisotropic capacity

CIRAOLO, Giulio;
2016

Abstract

We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in RN, establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of Reichel (Arch Ration Mech Anal 137(4):381–394, 1997), where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm H. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm H0).
http://link.springer-ny.com/link/service/journals/00526/index.htm
Bianchini, C., Ciraolo, G., & Salani, P. (2016). An overdetermined problem for the anisotropic capacity. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 55(4) [10.1007/s00526-016-1011-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/180774
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