On the first eigenvalue of a fourth order Steklov problem |
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Authors: | Dorin Bucur Alberto Ferrero Filippo Gazzola |
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Institution: | (1) Laboratoire de Mathématiques CNRS UMR 5127, Université de Savoie, 73376 Le-Bourget-Du-Lac, France;(2) Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, 20125 Milan, Italy;(3) Dipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy |
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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 ball. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35J40 65L15 |
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