Work

Boundary regularity and Hopf lemma for nondegenerate stable operators

Year: 2026

Type: article

Abstract: We prove sharp boundary Hölder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior C 1 , Dini -property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as s → 1 − and we recover the classical results for second order equations.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2026.111744

Author: Florian Grube

Institution: Bielefeld University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funder: Deutsche Forschungsgemeinschaft