We prove some results about the first Steklov eigenvalue d_1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d_1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ball
On the first eigenvalue of a fourth order Steklov problem
FERRERO, ALBERTO;
2009-01-01
Abstract
We prove some results about the first Steklov eigenvalue d_1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d_1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ballFile in questo prodotto:
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