Optimal stretching for lattice points and eigenvalues

DOI10.4310/ARKIV.2018.v56.n1.a8zbMath1390.35206arXiv1609.06172OpenAlexW2963255981MaRDI QIDQ1749369

Shiya Liu, Richard Snyder Laugesen

Publication date: 16 May 2018

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.06172

zbMATH Keywords

Dirichlet eigenvalueslattice pointsLaplacianplanar convex domainspectral optimizationNeumann eigenvalues\(p\)-ellipseLamé curve

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Lattice points in specified regions (11P21) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items (9)

TRIANGLES CAPTURING MANY LATTICE POINTS ⋮ Lattice points in stretched model domains of finite type in \(\mathbb{R}^d\) ⋮ Shifted lattices and asymptotically optimal ellipses ⋮ Pólya's conjecture for Euclidean balls ⋮ Asymptotic behaviour of cuboids optimising Laplacian eigenvalues ⋮ Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles ⋮ A note on lattice points and optimal stretching ⋮ Lattice points in stretched finite type domains ⋮ Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains

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