Gradient estimates for a class of anisotropic nonlocal operators

Alberto Farina (1) , Enrico Valdinoci

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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.

Domaines: Mathématiques [math]

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⟩