We consider overdetermined problems related to the fractional capacity. In particular we study s-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first classify the solutions of the overdetermined problems, by proving that the domain and the solution itself are radially symmetric. Then we prove a quantitative stability counterpart of the symmetry results: we assume that the overdetermined condition is slightly perturbed and we measure, in a quantitative way, how much the domain is close to a symmetric set. (c) 2023 Elsevier Inc. All rights reserved.
Quantitative results for fractional overdetermined problems in exterior and annular sets / G. Ciraolo, L. Pollastro. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 1096-0813. - 524:1(2023 Aug 01), pp. 127070.1-127070.18. [10.1016/j.jmaa.2023.127070]
Quantitative results for fractional overdetermined problems in exterior and annular sets
G. CiraoloCo-primo
;L. Pollastro
Co-primo
2023
Abstract
We consider overdetermined problems related to the fractional capacity. In particular we study s-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first classify the solutions of the overdetermined problems, by proving that the domain and the solution itself are radially symmetric. Then we prove a quantitative stability counterpart of the symmetry results: we assume that the overdetermined condition is slightly perturbed and we measure, in a quantitative way, how much the domain is close to a symmetric set. (c) 2023 Elsevier Inc. All rights reserved.File | Dimensione | Formato | |
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