2023/08/14 by Giorgio Poggesi, Poggesi, Giorgio · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2308.07000
openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We start providing a quantitative stability theorem for the rigidity of an overdetermined problem involving harmonic functions in a punctured domain. Our approach is inspired by and based on the proof of rigidity established by Enciso and Peralta-Salas, and reveals essential differences with respect to the stability results obtained in the literature for the classical overdetermined Serrin problem. Secondly, we provide new weighted Poincaré-type inequalities for vector fields. These are crucial tools for the study of the quantitative stability issue initiated by the author concerning a class of rigidity results involving mixed boundary value problems. Finally, we provide a mean value-type property and an associated weighted Poincaré-type inequality for harmonic functions in cones. A duality relation between this new mean value property and a partially overdetermined boundary value problem is discussed, providing an extension of a classical result due to Payne and Schaefer.