Work

Nonlinear nonlocal potential theory at the gradient level

Year: 2025

Type: article

Abstract: The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear nonlocal setting. First of all, we prove that weak solutions to a class of homogeneous nonlinear nonlocal equations of possibly arbitrarily low order have Hölder continuous gradients. Using these estimates in the homogeneous case, we then prove sharp higher differentiability as well as pointwise gradient potential estimates for nonlinear nonlocal equations of order larger than 1 in the presence of general measure data. Our pointwise estimates imply that the first-order regularity properties of such nonlinear nonlocal equations coincide with the sharp ones of the fractional Laplacian.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1706

Authors: Lars Diening, Kyeongbae Kim, Ho-Sik Lee, Simon Nowak

Institutions: Bielefeld University, Seoul National University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Research Foundation, Deutsche Forschungsgemeinschaft, Seoul National University, National Research Foundation of Korea