THE DIAGRAM (λ1, μ1)

Ftouhi I, Henrot A (2022)

Publication Language: English

Publication Type: Journal article

Publication year: 2022

Journal

Mathematical Reports Editura Academiei Romane

Book Volume: 24(74)

Pages Range: 159-177

Journal Issue: 1-2

URI: http://imar.ro/journals/Mathematical_Reports/Pdfs/2022/1-2/9.pdf

Abstract

In this paper we are interested in the possible values taken by the pair (λ1(ω), μ1(ω)) the first eigenvalues of the Laplace operator with Dirichlet and Neumann boundary conditions respectively of a bounded plane domain ω. We prove that, without any particular assumption on the class of open sets ω, the two classical inequalities (the Faber-Krahn inequality and the Weinberger inequality) provide a complete system of inequalities. Then we consider the case of convex plane domains for which we give new inequalities for the product λ1μ1. We plot the so-called Blaschke-Santaló diagram and give some conjectures.

Authors with CRIS profile

Ilias Ftouhi Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Université de Lorraine FR France (FR)

How to cite

APA:

Ftouhi, I., & Henrot, A. (2022). THE DIAGRAM (λ1, μ1). Mathematical Reports, 24(74)(1-2), 159-177.

MLA:

Ftouhi, Ilias, and Antoine Henrot. "THE DIAGRAM (λ1, μ1)." Mathematical Reports 24(74).1-2 (2022): 159-177.

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