Regularity for a fractional p-Laplace equation

Abstract

In this note we consider regularity theory for a fractional $p$-Laplace operator which arises in the complex interpolation of the Sobolev spaces, the $H^{s,p}$-Laplacian. We obtain the natural analogue to the classical $p$-Laplacian situation, namely $C_{loc}^{s+\alpha }$-regularity for the homogeneous equation.

References in corpus (8)

• Local behavior of fractional $p$-minimizers
• Nonlinear porous medium flow with fractional potential pressure
• Nonlocal porous medium equation: Barenblatt profiles and other weak solutions
• Nonlinear commutators for the fractional p-Laplacian and applications
• Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)
• ε-regularity for systems involving non-local, antisymmetric operators
• Integro-differential harmonic maps into spheres
• Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension

Cited by in corpus (5)

• A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
• A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I
• Calderon-Zygmund type estimates for nonlocal PDE with Hölder continuous kernel
• The fractional variation and the precise representative of $B{V}^{\alpha ,p}$ functions
• Leibniz rules and Gauss-Green formulas in distributional fractional spaces