Gradient estimates for a class of anisotropic nonlocal operators

2018/09/23 by Farina, Alberto, Valdinoci, Enrico
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.08674

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 Hölder estimates for the solution.

Related

• Gradient regularity and first-order potential estimates for a class of nonlocal equations
• Hölder estimates for nonlocal-diffusion equations with drifts
• Regularity results for nonlocal equations and applications
• Nonlinear nonlocal potential theory at the gradient level
• Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport