Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

Journal Article · Wed Feb 15 04:00:00 EST 2012 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-011-9153-X· OSTI ID:22043811

Hintermueller, M ^[1]; Laurain, A ^[2]

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1. Humboldt-University of Berlin (Germany)
2. Johann-von-Neumann-Haus, Department of Mathematics (Germany)

This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this threshold value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.

• OSTI ID: 22043811
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 65; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
BOUNDARY CONDITIONS
EIGENVALUES
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MINIMIZATION