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
Ferrero, A., Gazzola, F., Weth, T. (2005). On a fourth order Steklov eigenvalue problem. ANALYSIS, 25(38443), 315-332 [10.1524/anly.2005.25.4.315].
On a fourth order Steklov eigenvalue problem
FERRERO, ALBERTO;
2005
Abstract
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
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