The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization |
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| Authors: | Dorin Bucur Filippo Gazzola |
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| Institution: | 1.Laboratoire de Mathématiques (LAMA) UMR 5127,Université de Savoie – Campus Scientifique,Le-Bourget-Du-Lac,France;2.Dipartimento di Matematica,Politecnico di Milano,Milano,Italy |
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| Abstract: | We consider the Steklov problem for the linear biharmonic equation. We survey existing results for the positivity preserving
property to hold. These are connected with the first Steklov eigenvalue. We address the problem of minimizing this eigenvalue
among suitable classes of domains. We prove the existence of an optimal convex domain of fixed measure. |
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