The infinity Laplacian with a transport term

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Title: The infinity Laplacian with a transport term
Authors: López Soriano, Rafael | Navarro Climent, José Carlos | Rossi, Julio D.
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Infinity Laplacian | Tug of war games | Gradient terms
Knowledge Area: Análisis Matemático
Issue Date: 15-Feb-2013
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications. 2013, 398(2): 752-765. doi:10.1016/j.jmaa.2012.09.030
Abstract: We consider the following problem: given a bounded domain Ω⊂Rn and a vector field ζ:Ω→Rn, find a solution to −Δ∞u−〈Du,ζ〉=0 in Ω, u=f on ∂Ω, where Δ∞ is the 1-homogeneous infinity Laplace operator that is formally given by View the MathML source and f a Lipschitz boundary datum. If we assume that ζ is a continuous gradient vector field then we obtain the existence and uniqueness of a viscosity solution by an Lp-approximation procedure. Also we prove the stability of the unique solution with respect to ζ. In addition when ζ is more regular (Lipschitz continuous) but not necessarily a gradient, using tug-of-war games we prove that this problem has a solution.
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2012.09.030
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version:
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