Gradient estimates for a class of anisotropic nonlocal operators

Alberto Farina, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 Hölder estimates for the solution.

Original languageEnglish
Article number25
JournalNonlinear Differential Equations and Applications
Issue number4
Publication statusPublished - 1 Aug 2019


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