We consider the Wulff-type energy functional, (Formula Presented.) where B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential F(u) and we deduce several rigidity and symmetry properties.

Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations / M. Cozzi, A. Farina, E. Valdinoci. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 331:1(2014), pp. 189-214. [10.1007/s00220-014-2107-9]

Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations

M. Cozzi;E. Valdinoci
2014

Abstract

We consider the Wulff-type energy functional, (Formula Presented.) where B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential F(u) and we deduce several rigidity and symmetry properties.
nonnegative mean-curvature; elliptic-equations; unbounded-domains; crystal-growth; wulff shape; regularity; theorem
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/252352
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