The limit as p →∞ in free boundary problems with fractional p-laplacians

We study the p-fractional optimal design problem under volume constraint taking special care of the case when p is large, obtaining in the limit a free boundary problem modeled by the Hölder infinity Laplacian operator. A necessary and sufficient condition is imposed in order to obtain the uniquenes...

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Guardado en:
Detalles Bibliográficos
Publicado: 2019
Materias:
Fractional diffusion
Hölder infinity laplacian
Optimal design problems
Sharp regularity
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v371_n4_p2739_DASILVA
http://hdl.handle.net/20.500.12110/paper_00029947_v371_n4_p2739_DASILVA
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029947_v371_n4_p2739_DASILVA
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spelling paper:paper_00029947_v371_n4_p2739_DASILVA2023-06-08T14:23:41Z The limit as p →∞ in free boundary problems with fractional p-laplacians Fractional diffusion Hölder infinity laplacian Optimal design problems Sharp regularity We study the p-fractional optimal design problem under volume constraint taking special care of the case when p is large, obtaining in the limit a free boundary problem modeled by the Hölder infinity Laplacian operator. A necessary and sufficient condition is imposed in order to obtain the uniqueness of solutions to the limiting problem, and, under this condition, we find precisely the optimal configuration for the limit problem. We also prove the sharp regularity (locally C 0 ,s) for any limiting solution. Finally, we establish some geometric properties for solutions and their free boundaries. © 2018 American Mathematical Society. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v371_n4_p2739_DASILVA http://hdl.handle.net/20.500.12110/paper_00029947_v371_n4_p2739_DASILVA
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 diffusion
Hölder infinity laplacian
Optimal design problems
Sharp regularity
spellingShingle Fractional diffusion
Hölder infinity laplacian
Optimal design problems
Sharp regularity
The limit as p →∞ in free boundary problems with fractional p-laplacians
topic_facet Fractional diffusion
Hölder infinity laplacian
Optimal design problems
Sharp regularity
description We study the p-fractional optimal design problem under volume constraint taking special care of the case when p is large, obtaining in the limit a free boundary problem modeled by the Hölder infinity Laplacian operator. A necessary and sufficient condition is imposed in order to obtain the uniqueness of solutions to the limiting problem, and, under this condition, we find precisely the optimal configuration for the limit problem. We also prove the sharp regularity (locally C 0 ,s) for any limiting solution. Finally, we establish some geometric properties for solutions and their free boundaries. © 2018 American Mathematical Society.
title The limit as p →∞ in free boundary problems with fractional p-laplacians
title_short The limit as p →∞ in free boundary problems with fractional p-laplacians
title_full The limit as p →∞ in free boundary problems with fractional p-laplacians
title_fullStr The limit as p →∞ in free boundary problems with fractional p-laplacians
title_full_unstemmed The limit as p →∞ in free boundary problems with fractional p-laplacians
title_sort limit as p →∞ in free boundary problems with fractional p-laplacians
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v371_n4_p2739_DASILVA
http://hdl.handle.net/20.500.12110/paper_00029947_v371_n4_p2739_DASILVA
_version_ 1768546280313716736

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