Blaschke–Santaló and Mahler inequalities for the first eigenvalue of the Dirichlet Laplacian

DOI10.1112/plms/pdw032zbMath1361.49019OpenAlexW2504651294MaRDI QIDQ2832000

Dorin Bucur, Ilaria Fragalà

Publication date: 4 November 2016

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/pdw032

zbMATH Keywords

first Dirichlet eigenvalueMahler inequality\(\lambda_1\) product functionalBlaschke-Santalo's inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Optimization of shapes other than minimal surfaces (49Q10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Variational methods for eigenvalues of operators (49R05)

Related Items

On the polygonal Faber-Krahn inequality ⋮ Polygons as maximizers of Dirichlet energy or first eigenvalue of Dirichlet-Laplacian among convex planar domains ⋮ From affine Poincaré inequalities to affine spectral inequalities

Uses Software

• Matlab
• Partial Differential Equation Toolbox

Cites Work

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