Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions

In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal to a prescribed quantity α). We show...

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Detalles Bibliográficos
Publicado: 2018
Materias:
Fractional Laplacian
Gamma Convergence
Shape Optimization
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n2_p323_FernandezBonder
http://hdl.handle.net/20.500.12110/paper_15361365_v18_n2_p323_FernandezBonder
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15361365_v18_n2_p323_FernandezBonder
record_format dspace
spelling paper:paper_15361365_v18_n2_p323_FernandezBonder2023-06-08T16:20:11Z Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions Fractional Laplacian Gamma Convergence Shape Optimization In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal to a prescribed quantity α). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter s converges to 1, and thus obtain asymptotic bounds that are independent of α. © 2018 Walter de Gruyter GmbH, Berlin/Boston 2018. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n2_p323_FernandezBonder http://hdl.handle.net/20.500.12110/paper_15361365_v18_n2_p323_FernandezBonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fractional Laplacian
Gamma Convergence
Shape Optimization
spellingShingle Fractional Laplacian
Gamma Convergence
Shape Optimization
Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
topic_facet Fractional Laplacian
Gamma Convergence
Shape Optimization
description In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal to a prescribed quantity α). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter s converges to 1, and thus obtain asymptotic bounds that are independent of α. © 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.
title Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
title_short Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
title_full Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
title_fullStr Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
title_full_unstemmed Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions
title_sort optimal design problems for the first p-fractional eigenvalue with mixed boundary conditions
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n2_p323_FernandezBonder
http://hdl.handle.net/20.500.12110/paper_15361365_v18_n2_p323_FernandezBonder
_version_ 1768543248281763840

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