On a fourth order Steklov eigenvalue problem

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.