Work

Quantitative stability for the nonlocal overdetermined Serrin problem

Year: 2026

Type: article

Abstract: We establish quantitative stability for the nonlocal Serrin overdetermined problem, via the method of the moving planes. Interestingly, our stability estimate is even better than those obtained so far in the classical setting (i.e., for the classical Laplacian) via the method of the moving planes. A crucial ingredient is the construction of a new antisymmetric barrier, which allows a unified treatment of the moving planes method. This strategy allows us to establish a new general quantitative nonlocal maximum principle for antisymmetric functions, leading to new quantitative nonlocal versions of both the Hopf lemma and the Serrin corner point lemma. All these tools – i.e., the new antisymmetric barrier, the general quantitative nonlocal maximum principle, and the quantitative nonlocal versions of both the Hopf lemma and the Serrin corner point lemma – are of independent interest.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2026.111243

Authors: Serena Dipierro, Giorgio Poggesi, Jack Thompson, Enrico Valdinoci

Institutions: The University of Western Australia, Adelaide University, The University of Adelaide

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Australian Government, Australian Mathematical Society, Australian Research Council