Gradient regularity and first-order potential estimates for a class of nonlocal equations

T Kuusi, S Nowak, Y Sire - arXiv preprint arXiv:2212.01950, 2022 - arxiv.org
We consider nonlocal equations of order larger than one with measure data and prove
gradient regularity in Sobolev and H\" older spaces as well as pointwise bounds of the …

Optimal boundary regularity and Green function estimates for nonlocal equations in divergence form

M Kim, M Weidner - arXiv preprint arXiv:2408.12987, 2024 - arxiv.org
In this article we prove for the first time the $ C^ s $ boundary regularity for solutions to
nonlocal elliptic equations with H\" older continuous coefficients in divergence form in …

[HTML][HTML] Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities

M Bonforte, J Endal - Journal of Functional Analysis, 2023 - Elsevier
We establish boundedness estimates for solutions of generalized porous medium equations
of the form∂ t u+(− L)[um]= 0 in RN×(0, T), where m≥ 1 and− L is a linear, symmetric, and …