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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029947_v371_n4_p2739_DASILVA |
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todo:paper_00029947_v371_n4_p2739_DASILVA2023-10-03T13:55:24Z The limit as p →∞ in free boundary problems with fractional p-laplacians DA SILVA, J.V. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 DA SILVA, J.V. Rossi, J.D. 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. |
| format |
JOUR |
| author |
DA SILVA, J.V. Rossi, J.D. |
| author_facet |
DA SILVA, J.V. Rossi, J.D. |
| author_sort |
DA SILVA, J.V. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00029947_v371_n4_p2739_DASILVA |
| work_keys_str_mv |
AT dasilvajv thelimitaspinfreeboundaryproblemswithfractionalplaplacians AT rossijd thelimitaspinfreeboundaryproblemswithfractionalplaplacians AT dasilvajv limitaspinfreeboundaryproblemswithfractionalplaplacians AT rossijd limitaspinfreeboundaryproblemswithfractionalplaplacians |
| _version_ |
1782026289646927872 |