Differential equations with singular fields |
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Authors: | Pierre-Emmanuel Jabin |
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Institution: | aEquipe Tosca, Inria, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis, France;bLaboratoire Dieudonné, Univ. de Nice, Parc Valrose, 06108 Nice cedex 02, France |
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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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Keywords: | MSC: 34C11 35L45 37C10 |
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