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Alberto Ferrero, Filippo Gazzola, Tobias Weth

On a fourth order Steklov eigenvalue problem

Keywords: biharmonic operator, eigenvalues problems, shape optimization

We study the spectrum of a biharmonic Steklov eigenvalue problem in a bounded domain of Rⁿ. We characterize it in general and give its explicit form in the case where the domain is a ball. Then, we focus our attention on the first eigenvalue of this problem. We prove some estimates and study its isoperimetric properties. By recalling a number of known results, we finally highlight the main open problems still to be solved.

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 25, 04/2005
Pages: 315 - 332

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