Two Estimates for the First Robin Eigenvalue of the Finsler Laplacian with Negative Boundary Parameter

We prove two bounds for the first Robin eigenvalue of the Finsler Laplacian with negative boundary parameter in the planar case. In the constant area problem, we show that the Wulff shape is a maximizer only for values of the boundary parameter, which are close to zero. In the fixed perimeter case,...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2019-06, Vol.181 (3), p.743-757
Main Authors: Paoli, Gloria, Trani, Leonardo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Eigenvalues
Engineering
Laplace transforms
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Parameters
Theory of Computation
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Summary:We prove two bounds for the first Robin eigenvalue of the Finsler Laplacian with negative boundary parameter in the planar case. In the constant area problem, we show that the Wulff shape is a maximizer only for values of the boundary parameter, which are close to zero. In the fixed perimeter case, we prove that the Wulff shape is a maximizer of the first eigenvalue for all values of the boundary parameter.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-019-01487-x