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- W4385849114 abstract "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 Poincar'e-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 Poincar'e-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." @default.
- W4385849114 created "2023-08-16" @default.
- W4385849114 creator A5065088713 @default.
- W4385849114 date "2023-08-14" @default.
- W4385849114 modified "2023-09-26" @default.
- W4385849114 title "Remarks about the mean value property and some weighted Poincar'e-type inequalities" @default.
- W4385849114 doi "https://doi.org/10.48550/arxiv.2308.07000" @default.
- W4385849114 hasPublicationYear "2023" @default.
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