THE DIAGRAM (lambda(1), mu(1))
Ftouhi I, Henrot A (2022)
Publication Type: Journal article
Publication year: 2022
Journal
Book Volume: 24
Pages Range: 159-177
Journal Issue: 1-2
Abstract
In this paper we are interested in the possible values taken by the pair (lambda(1) (Omega); mu(1)(Omega)) the first eigenvalues of the Laplace operator with Dirichlet and Neumann boundary conditions respectively of a bounded plane domain Omega. We prove that, without any particular assumption on the class of open sets Omega, 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 lambda(1)mu(1). We plot the so-called Blaschke-Santalo diagram and give some conjectures.
Involved external institutions
France (FR)How to cite
APA:
Ftouhi, I., & Henrot, A. (2022). THE DIAGRAM (lambda(1), mu(1)). Mathematical Reports, 24(1-2), 159-177.
MLA:
Ftouhi, Ilias, and Antoine Henrot. "THE DIAGRAM (lambda(1), mu(1))." Mathematical Reports 24.1-2 (2022): 159-177.
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