A unified treatment of ODEs under Osgood and Sobolev type conditions

Published 13 Jul 2011 in math.CA | (1107.2496v2)

Abstract: In this paper we present a unified treatment for the ordinary differential equations under the Osgood and Sobolev type conditions, following Crippa and de Lellis's direct method. More precisely, we prove the existence, uniqueness and regularity of the DiPerna-Lions flow generated by a vector field which is "almost everywhere Osgood continuous".

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