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dc.contributor.author
Blanc, Pablo
dc.contributor.author
Pinasco, Juan Pablo
dc.contributor.author
Rossi, Julio Daniel
dc.date.available
2018-08-14T17:48:20Z
dc.date.issued
2017-04
dc.identifier.citation
Blanc, Pablo; Pinasco, Juan Pablo; Rossi, Julio Daniel; Maximal operators for the P-laplacian family; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 287; 2; 4-2017; 257-295
dc.identifier.issn
0030-8730
dc.identifier.uri
http://hdl.handle.net/11336/55434
dc.description.abstract
We prove existence and uniqueness of viscosity solutions for the problem: max-Δp1u(x), -Δp2u(x) = f(x) in a bounded smooth domain Ω⊂ℝN with u=g on ∂Ω. Here -Δpu=(N+ p)-1|Du|2-pdiv (|Du|p-2Du) is the 1-homogeneous p-Laplacian and we assume that 2 ≤ p1; p2 ≤ ∞. This equation appears naturally when one considers a tug-of-war game in which one of the players (the one who seeks to maximize the payoff ) can choose at every step which are the parameters of the game that regulate the probability of playing a usual tug-ofwar game (without noise) or playing at random. Moreover, the operator max-Δp1u(x), -Δp2u(x) provides a natural analogue with respect to p- Laplacians to the Pucci maximal operator for uniformly elliptic operators. We provide two different proofs of existence and uniqueness for this problem. The first one is based in pure PDE methods (in the framework of viscosity solutions) while the second one is more connected to probability and uses game theory.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Pacific Journal Mathematics
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Dirichlet Boundary Conditions
dc.subject
Dynamic Programming Principle
dc.subject
P-Laplacian
dc.subject
Tug-Of-War Games
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Maximal operators for the P-laplacian family
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-14T13:58:16Z
dc.journal.volume
287
dc.journal.number
2
dc.journal.pagination
257-295
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Los Angeles
dc.description.fil
Fil: Blanc, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Pinasco, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.journal.title
Pacific Journal Of Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://dx.doi.org/10.2140/pjm.2017.287.257
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://msp.org/pjm/2017/287-2/p01.xhtml


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