We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated wisted"problem, we show that, this problem displays a saturation phenomenon: The first eigenvalue increases with the weight up to a critical value and then remains constant.
A nonlocal anisotropic eigenvalue problem / Piscitelli, G.. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - 29:11-12(2016), pp. 1001-1020.
A nonlocal anisotropic eigenvalue problem
Piscitelli G.
2016
Abstract
We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated wisted"problem, we show that, this problem displays a saturation phenomenon: The first eigenvalue increases with the weight up to a critical value and then remains constant.File in questo prodotto:
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