Differential equations with singular fields

Pierre-Emmanuel Jabin 1, 2
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : This paper investigates the well posedness of ordinary differential equations and more precisely the existence (or uniqueness) of a flow through explicit compactness estimates. Instead of assuming a bounded divergence condition on the vector field, a compressibility condition on the flow (bounded Jacobian) is considered. The main result provides existence under the condition that the vector field belongs to BV in dimension 2 and SBV in higher dimensions.
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Submitted on : Tuesday, June 21, 2011 - 10:43:25 AM
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Pierre-Emmanuel Jabin. Differential equations with singular fields. Journal de Mathématiques Pures et Appliquées, Elsevier, 2010, 94 (6), pp.597-621. ⟨10.1016/j.matpur.2010.07.001⟩. ⟨hal-00601959⟩



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