On the Geometry of Optimal Windows, with Special Focus on the Square

For the Laplace operator with mixed (Dirichlet and Neumann) boundary conditions, the dependence of the principal eigenvalue on the placement of the Dirichlet part is investigated. An optimal window is a Dirichlet part of the boundary that minimizes the principal eigenvalue among all competitors of t...

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Bibliographic Details
Published in:	SIAM journal on mathematical analysis Vol. 37; no. 6; pp. 1800 - 1827
Main Authors:	Burchard, Almut, Denzler, Jochen
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2006
Subjects:	Applied mathematics Boundary conditions Calculus of variations and optimal control Eigenvalues Exact sciences and technology Geometry Heat Mathematical analysis Mathematics Partial differential equations Potential theory Sciences and techniques of general use Laplace operator Discontinuity Neumann problem Singularity Variational methods 31C40 shape optimization Eigenfunction Optimization method Optimal eigenvalue 35J05 Boundary condition mixed boundary conditions singular coefficient Capacity rearrangement; 49R50 Dirichlet problem 35R05
ISSN:	0036-1410, 1095-7154
Online Access:	Get full text
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