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Isotropic stochastic flow of homeomorphisms on Sd for the critical Sobolev exponent

2006

Abstract In this work, we shall deal with the critical Sobolev isotropic Brownian flows on the sphere S d . Based on previous works by O. Raimond and LeJan and Raimond (see [O. Raimond, Ann. Inst. H. Poincare 35 (1999) 313–354] and [Y. LeJan, O. Raimond, Ann. of Prob. 30 (2002) 826–873], we prove that the associated flows are flows of homeomorphisms.

Sobolev exponentKolmogoroff modification theoremApplied MathematicsGeneral MathematicsEigenvectorIsotropyMathematical analysisSpherical representationHomeomorphismNon-Lipschitzian conditionSobolev spacesymbols.namesakeLaplace operatorMathematics::ProbabilityPoincaré conjecturesymbolsExponentIsotropic flowsLaplace operatorCritical exponentBrownian motionMathematicsJournal de Mathématiques Pures et Appliquées
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