Work

Gradient estimates for parabolic nonlinear nonlocal equations

Year: 2025

Type: article

Abstract: The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms of caloric Riesz potentials of the data. As a consequence of our pointwise estimates, we obtain that the first-order regularity properties of solutions to such general parabolic nonlinear nonlocal equations, both in terms of size and oscillations of the spatial gradient, closely resemble the ones of the fractional heat equation even at highly refined scales. Along the way, we show that solutions to homogeneous parabolic nonlinear nonlocal equations have Hölder continuous spatial gradients under optimal assumptions on the nonlocal tails.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-02957-z

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: hybrid

Estimated APC paid: $3,190