A unified treatment of ODEs under Osgood and Sobolev type conditions
Classical Analysis and ODEs
2015-03-03 v2
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".
Keywords
Cite
@article{arxiv.1107.2496,
title = {A unified treatment of ODEs under Osgood and Sobolev type conditions},
author = {Huaiqian Li and Dejun Luo},
journal= {arXiv preprint arXiv:1107.2496},
year = {2015}
}
Comments
15 pages, an example of vector fields satisfying (1.4) is given