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

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Date
2013
Volume
1803
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We consider the Wulff-type energy functional 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.

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Keywords
Crystal growth, pointwise estimates, rigidity and symmetry results
Citation
Cozzi, M., Farina, A., & Valdinoci, E. (2013). Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations (Vol. 1803). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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