Minimization problems for eigenvalues of the Laplacian

Antoine Henrot ()
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Antoine Henrot: INRIA, Ecole des Mines and Institut Elie Cartan Nancy UMR 7502 CNRS and projet Corida

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 443-461 from Springer

Abstract: Abstract This paper is a survey on classical results and open questions about minimization problems concerning the lower eigenvalues of the Laplace operator. After recalling classical isoperimetric inequalities for the two first eigenvalues, we present recent advances on this topic. In particular, we study the minimization of the second eigenvalue among plane convex domains. We also discuss the minimization of the third eigenvalue. We prove existence of a minimizer. For others eigenvalues, we just give some conjectures. We also consider the case of Neumann, Robin and Stekloff boundary conditions together with various functions of the eigenvalues.

Keywords: 49Q10; 35P15; 49J20; Eigenvalues; minimization; isoperimetric inequalities; optimal domain (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_24

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DOI: 10.1007/978-3-0348-7924-8_24

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