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- W2895537029 abstract "These lecture notes give an overview of “isoperimetric inequalities”, namely inequalities involving only geometric features, for the eigenvalues of the Laplace operator, with Dirichlet boundary conditions. In other words, we are mainly interested in minimization problems like 2.1 $$displaystyle begin{aligned} text{min} {lambda_k(varOmega),;varOmegasubset mathbb{R}^N mbox{ open set, with some geometric constraints. }} end{aligned} $$ Here λ k(Ω) denotes the k-th eigenvalue of the Laplace operator with Dirichlet boundary conditions and the geometric constraints can involve the volume or the perimeter or the diameter or some box constraints or some specific sub-classes like polygons or convex sets. Most of the information contained in these notes are from the book of the author (Henrot, Extremum problems for eigenvalues of elliptic operators. Frontiers in mathematics, Birkhäuser, Basel, 2006), but some more recent results are also presented." @default.
- W2895537029 created "2018-10-12" @default.
- W2895537029 creator A5046029162 @default.
- W2895537029 date "2018-01-01" @default.
- W2895537029 modified "2023-10-09" @default.
- W2895537029 title "Isoperimetric Inequalities for Eigenvalues of the Laplacian" @default.
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- W2895537029 doi "https://doi.org/10.1007/978-3-319-95186-7_2" @default.
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