Minimization problems for eigenvalues of the Laplacian

By Antoine Henrot. 2003

95 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a07506d336baf07045f79ac4ecd498a8c87f407

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A Faber-Krahn inequality for Robin problems in any space dimension (2006, background): “If β = 0, then λ1(Ω ) = 0 for all bounded domains Ω , so the question we ask is not very interesting and other questions become relevant (see for instance [4,18,27]).”
Rearrangement inequalities and applications to isoperimetric problems for eigenvalues (2006, background): “Much more complete surveys of all these topics can be found in [11, 25, 26].”
Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold (2007, background): “Extensions of this classical result to higher order eigenvalues, combinations of eigenvalues as well as domains of other Riemannian manifolds or subjected to other types of constraints, have been obtained during the last decades and a very rich literature is devoted to this subject (see for instance”
Isogeometric Shape Optimization of Vibrating Membranes (2011, methodology): “We treat vibrating membranes as as a model problem for more general spectral shape optimization problems of systems governed by elliptic operators [15, 16].”
Existence of minimizers for spectral problems (2011, background): “For other open problems and partial results see [7, 2].”
Numerical minimization of eigenmodes of a membrane with respect to the domain (2004, unknown): “For k ≥ 3 fixed, the question to identify the open set of the plane which minimizes λk amongst the sets of given area remains open today (see [10] for a survey on this subject).”
Minimizing the Second Eigenvalue of the Laplace Operator with Dirichlet Boundary Conditions (2003, background): “to [5], [32] and the review papers [2], [4], [ 17 ].”
Isoperimetric Inequalities for Eigenvalues of the Laplacian (2007, background): “Some further discussion occurs in Henrot’s paper [82], pp.”