The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is L...
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2014
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v56_n2_p241_Navarro http://hdl.handle.net/20.500.12110/paper_00170895_v56_n2_p241_Navarro |
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| Sumario: | In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is Lipschitz continuous but not differentiable when we consider deformations obtained via a vector field. Our results are illustrated with simple examples. © Glasgow Mathematical Journal Trust 2013. |
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