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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
dc.conicet.fuente individual


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    Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"

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info:eu-repo/semantics/restrictedAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)