2023/09/29 by Serena Dipierro, Giorgio Poggesi, Dipierro, Serena +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2309.17119
openalex publication_date 2023/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.