dc.contributor.author Souganidis, Panagiotis E. * dc.contributor.author Lions, Pierre-Louis * dc.date.accessioned 2012-02-28T13:17:31Z dc.date.available 2012-02-28T13:17:31Z dc.date.issued 2010 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/8307 dc.language.iso en en dc.subject viscosity solutions en dc.subject Hamilton-Jacobi equations en dc.subject Stochastic homogenization en dc.subject.ddc 519 en dc.title Stochastic homogenization of Hamilton-Jacobi and "Viscous"-Hamilton-Jacobi equations with convex en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Department of mathematics http://www.math.uchicago.edu/ Université de Chicago;États-Unis dc.description.abstracten In this note we revisit the homogenization theory of Hamilton-Jacobi and “viscous”- Hamilton-Jacobi partial differential equations with convex nonlinearities in stationary ergodic envi- ronments. We present a new simple proof for the homogenization in probability. The argument uses some a priori bounds (uniform modulus of continuity) on the solution and the convexity and coer- civity (growth) of the nonlinearity. It does not rely, however, on the control interpretation formula of the solution as was the case with all previously known proofs. We also introduce a new formula for the effective Hamiltonian for Hamilton-Jacobi and “viscous” Hamilton-Jacobi equations. en dc.relation.isversionofjnlname Communications in Mathematical Sciences dc.relation.isversionofjnlvol 8 en dc.relation.isversionofjnlissue 2 en dc.relation.isversionofjnldate 2010 dc.relation.isversionofjnlpages 627-637 en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher International Press en dc.subject.ddclabel Probabilités et mathématiques appliquées en hal.person.labIds * hal.person.labIds *
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