Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order

Abstract

We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequality, a weak Harnack inequality, and a local Hölder estimate.

28 pages, 2 figures, slight modifications and corrections

References in corpus (4)

• Nonlocal equations with measure data
• Three representations of the fractional $p$-Laplacian: semigroup, extension and Balakrishnan formulas
• On a Class of Nonlocal Obstacle Type Problems Related to the Distributional Riesz Fractional Derivative
• Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic $p$-Laplace equation

Cited by in corpus (4)

• The Wiener criterion for nonlocal Dirichlet problems
• The concentration-compactness principle for the nonlocal anisotropic $p$-Laplacian of mixed order
• Local Hölder regularity for nonlocal equations with variable powers
• Local Hölder Regularity for Quasilinear Elliptic Equations with Mixed Local-Nonlocal Operators, Variable Exponents, and Weights