Sharp gradient integrability for $(s,p)$-Poisson type equations
Analysis of PDEs
2026-02-10 v1
Abstract
We prove local -regularity for weak solutions to fractional -Laplacian type equations with right-hand side . Assuming , , and , solutions belong to for the optimal exponent . We obtain quantitative local gradient estimates involving nonlocal tail terms. The optimality of is confirmed by a counterexample.
Cite
@article{arxiv.2602.08944,
title = {Sharp gradient integrability for $(s,p)$-Poisson type equations},
author = {Verena Bögelein and Frank Duzaar and Naian Liao and Kristian Moring},
journal= {arXiv preprint arXiv:2602.08944},
year = {2026}
}