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arXiv · 1809.08674

Gradient estimates for a class of anisotropic nonlocal operators

Alberto Farina·Enrico Valdinoci
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Abstract

Using a classical technique introduced by Achi E. Brandt for elliptic equations, we study a general class of nonlocal equations obtained as a superposition of classical and fractional operators in different variables. We obtain that the increments of the derivative of the solution in the direction of a variable experiencing classical diffusion are controlled linearly, with a logarithmic correction. From this, we obtain H\"older estimates for the solution.

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Alberto Farina, Enrico Valdinoci. 2018-09-23. Gradient estimates for a class of anisotropic nonlocal operators. https://arxiv.org/abs/1809.08674

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