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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Vydané v:	Journal of mathematical analysis and applications Ročník 505; číslo 2; s. 125531
Hlavní autori:	Gilsbach, Alexandra, Stollenwerk, Kathrin
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 15.01.2022
Predmet:	Biharmonic operator Implicit function theorem Overdetermined problem Stability estimates Implicit function theorem Overdetermined problem Stability estimates Biharmonic operator
ISSN:	0022-247X, 1096-0813
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Popis
Shrnutí:	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