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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2019
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| 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 |
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| Sumario: | 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. |
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