Obstacle Problems and Maximal Operators

Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li ( i=1,2${i=1,2}$ alternating them) with obstacle given by the...

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Autores principales: Pinasco, Juan Pablo, Rossi, Julio Daniel
Publicado: 2016
Materias:
Dirichlet Boundary Conditions
Maximal Operators
Obstacle Problems
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v16_n2_p355_Blanc
http://hdl.handle.net/20.500.12110/paper_15361365_v16_n2_p355_Blanc
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15361365_v16_n2_p355_Blanc
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spelling paper:paper_15361365_v16_n2_p355_Blanc2023-06-08T16:20:10Z Obstacle Problems and Maximal Operators Pinasco, Juan Pablo Rossi, Julio Daniel Dirichlet Boundary Conditions Maximal Operators Obstacle Problems Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li ( i=1,2${i=1,2}$ alternating them) with obstacle given by the previous term un-1 in a domain Ω and a fixed boundary datum g on Ω${\\partial \\Omega }$ . We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L 1 u,L 2 u}=0${\\min \\lbrace L-1 u, L-2 u \\rbrace =0}$ in Ω with u=g${u=g}$ on Ω${\\partial \\Omega }$ . © 2016 by De Gruyter. Fil:Pinasco, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v16_n2_p355_Blanc http://hdl.handle.net/20.500.12110/paper_15361365_v16_n2_p355_Blanc
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Dirichlet Boundary Conditions
Maximal Operators
Obstacle Problems
spellingShingle Dirichlet Boundary Conditions
Maximal Operators
Obstacle Problems
Pinasco, Juan Pablo
Rossi, Julio Daniel
Obstacle Problems and Maximal Operators
topic_facet Dirichlet Boundary Conditions
Maximal Operators
Obstacle Problems
description Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li ( i=1,2${i=1,2}$ alternating them) with obstacle given by the previous term un-1 in a domain Ω and a fixed boundary datum g on Ω${\\partial \\Omega }$ . We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L 1 u,L 2 u}=0${\\min \\lbrace L-1 u, L-2 u \\rbrace =0}$ in Ω with u=g${u=g}$ on Ω${\\partial \\Omega }$ . © 2016 by De Gruyter.
author Pinasco, Juan Pablo
Rossi, Julio Daniel
author_facet Pinasco, Juan Pablo
Rossi, Julio Daniel
author_sort Pinasco, Juan Pablo
title Obstacle Problems and Maximal Operators
title_short Obstacle Problems and Maximal Operators
title_full Obstacle Problems and Maximal Operators
title_fullStr Obstacle Problems and Maximal Operators
title_full_unstemmed Obstacle Problems and Maximal Operators
title_sort obstacle problems and maximal operators
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v16_n2_p355_Blanc
http://hdl.handle.net/20.500.12110/paper_15361365_v16_n2_p355_Blanc
work_keys_str_mv AT pinascojuanpablo obstacleproblemsandmaximaloperators
AT rossijuliodaniel obstacleproblemsandmaximaloperators
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