Existence and stability of solutions for a fourth order overdetermined problem

We examine a Serrin-type overdetermined boundary value problem for the biharmonic operator. If the underlying set is the unit ball, a solution exists for a constant overdetermining condition. We prove the existence of an open and bounded domain admitting a solution to the boundary value problem for...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 505; no. 2; p. 125531
Main Authors: Gilsbach, Alexandra, Stollenwerk, Kathrin
Format: Journal Article
Language:English
Published: Elsevier Inc 15.01.2022
Subjects:
Biharmonic operator
Implicit function theorem
Overdetermined problem
Stability estimates
Implicit function theorem
Overdetermined problem
Stability estimates
Biharmonic operator
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:We examine a Serrin-type overdetermined boundary value problem for the biharmonic operator. If the underlying set is the unit ball, a solution exists for a constant overdetermining condition. We prove the existence of an open and bounded domain admitting a solution to the boundary value problem for every small perturbation of the overdetermining condition. Moreover, we establish stability estimates for the deviation of this domain from the unit ball in terms of the perturbation. Our approach is motivated by a recent result of Gilsbach and Onodera and applies a result of Ferrero, Gazzola and Weth for a fourth order Steklov problem.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125531