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dc.contributor.authorLions, Pierre-Louis
dc.contributor.authorLe Bris, Claude
dc.contributor.authorBlanc, Xavier
dc.date.accessioned2010-01-18T10:22:11Z
dc.date.available2010-01-18T10:22:11Z
dc.date.issued2007-04
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3012
dc.description.abstractfrWe present some variants of stochastic homogenization theory for scalar elliptic equations of the form−div[A( x ε ,ω)∇u(x,ω)]= f . These variants basically consist in defining stochastic coefficients A( x ε ,ω) from stochastic deformations (using random diffeomorphisms) of the periodic setting, as announced in [X. Blanc, C. Le Bris, P.-L. Lions, Une variante de la théorie de l’homogénéisation stochastique des opérateurs elliptiques (A variant of stochastic homogenization theory for elliptic operators), C. R. Acad. Sci. Sér. I 343 (2006) 717–727]. The settings we define are not covered by the existing theories. We also clarify the relation between this type of questions and our construction, performed in [X. Blanc, C. Le Bris, P.-L. Lions, A definition of the ground state energy for systems composed of infinitely many particles, Commun. Partial Differential Equations 28 (1–2) (2003) 439–475; X. Blanc, C. Le Bris, P.-L. Lions, The energy of some microscopic stochastic lattices, Arch. Rat. Mech. Anal. 184 (2) (2007) 303–339], of the energy of, both deterministic and stochastic, microscopic infinite sets of points in interaction.en
dc.language.isoenen
dc.subjectThermodynamiqueen
dc.subjectEquation différentielleen
dc.subjectEquation dérivée partielleen
dc.subjectDifferential equationen
dc.subjectHomogenizationen
dc.subjectElliptic operatoren
dc.subject.ddc515en
dc.titleStochastic homogenization and random latticesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherINRIA Rocquencourt;France
dc.contributor.editoruniversityotherCollège de France, Paris;France
dc.contributor.editoruniversityotherÉcole Nationale des Ponts et Chaussées, Marne la Vallée;France
dc.description.abstractenWe present some variants of stochastic homogenization theory for scalar elliptic equations of the form -div[ A(x/ε,ω) ∇ u] = f. These variants basically consist in defining stochastic coefficients A(x/ε,ω) from stochastic deformations (using random diffeormorphisms) of the periodic setting, as announced in [4]. The settings we define are not covered by the existing theories. We also clarify the relation between this type of questions and our construction, performed in [3,5], of the energy of, both deterministic and stochastic, microscopic infinite sets of points in interaction.en
dc.relation.isversionofjnlnameJournal de mathématiques pures et appliquées
dc.relation.isversionofjnlvol88en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages34-63en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.matpur.2007.04.006en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen


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