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@article{faucris.285701747,
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.},
author = {Ftouhi, Ilias and Henrot, Antoine},
faupublication = {yes},
journal = {Mathematical Reports},
month = {Jan},
note = {CRIS-Team WoS Importer:2022-11-25},
pages = {159-177},
peerreviewed = {Yes},
title = {{THE} {DIAGRAM} (lambda(1), mu(1))},
volume = {24},
year = {2022}
}