Work

Semiconvexity estimates for nonlinear integro‐differential equations

Year: 2024

Type: article

Abstract: In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro‐differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators and consider to be of independent interest. In particular, we solve an open problem from Cabré‐Dipierro‐Valdinoci. As an application of our result, we establish optimal regularity estimates and smoothness of the free boundary near regular points for the nonlocal obstacle problem on domains. Finally, we also extend the Bernstein technique to parabolic equations and nonsymmetric operators.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.22237

Authors: Xavier Ros‐Oton, Clara Torres‐Latorre, Marvin Weidner

Institutions: Institució Catalana de Recerca i Estudis Avançats, Centre de Recerca Matemàtica, Universitat de Barcelona, Institute of Mathematical Sciences

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,980

Funders: Schweizerische Gesellschaft für Radiologie, European Research Council, Agencia Estatal de Investigación