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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2019

Gradient estimates for a class of anisotropic nonlocal operators

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Résumé

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 Holder estimates for the solution.

Dates et versions

hal-03621409 , version 1 (28-03-2022)

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Alberto Farina, Enrico Valdinoci. Gradient estimates for a class of anisotropic nonlocal operators. Nonlinear Differential Equations and Applications, 2019, 26 (4), ⟨10.1007/s00030-019-0571-9⟩. ⟨hal-03621409⟩
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