On the first eigenvalue and eigenfunction of the Laplacian with mixed boundary conditions

We consider the eigenvalue problem for the Laplacian with mixed Dirichlet and Neumann boundary conditions. For a certain class of bounded, simply connected planar domains we prove monotonicity properties of the first eigenfunction. As a consequence, we establish a variant of the hot spots conjecture...

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Bibliographic Details

Published in:	Journal of Differential Equations Vol. 427; pp. 689 - 718
Main Authors:	Aldeghi, Nausica, Rohleder, Jonathan
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.05.2025
Subjects:	Eigenfunctions Eigenvalue inequalities Hot spots Laplacian matematik Mathematics Mixed boundary conditions Variational principles Eigenfunctions Mixed boundary conditions Variational principles Hot spots Laplacian Eigenvalue inequalities
ISSN:	0022-0396, 1090-2732
Online Access:	Get full text
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