A few remarks on ordinary differential equations
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 21 (11) , 1667-1703
- https://doi.org/10.1080/03605309608821242
Abstract
We present in this note existence and uniqueness results for solutions of ordinary differential equations and linear transport equations with discontinuous coefficients in a bounded open subset Ωof RN or in the whole space RN(N≥1). R.J.Di Perna and P.L.Lions studied the case of vector fields b with coefficients in Sobolev spaces and bounded divergence. We want to show that similat results hold for more general b: we assume in the bounded autonomous case that b belongs to and that there exists suchthat . Furthermore, we establish results on transport equations with initial values in Lp spaces(p1).Keywords
This publication has 2 references indexed in Scilit:
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- Ordinary differential equations, transport theory and Sobolev spacesInventiones Mathematicae, 1989