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Asymptotic spherical shapes in some spectral optimization problems
[article]
2019
arXiv
pre-print
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box Ω⊂R^N, which arises in the investigation of the survival threshold in population dynamics. When trying to minimize such eigenvalue with respect to the weight, one is lead to consider a shape optimization problem, which is known to admit no spherical optimal shapes (despite some previously stated conjectures). We investigate whether spherical shapes can
arXiv:1811.01623v3
fatcat:cytubb2s2rea5d52bg3hcxzvoa