A generalized Cauchy-Lipschitz theorem in low regularity spaces
Functional Analysis
2017-09-28 v4 Analysis of PDEs
Abstract
We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with low regularity indexes. The loss of derivatives induced by such operators has to be lower than one, in order to be dominated by the first order derivative involved in the problem.
Cite
@article{arxiv.1701.02636,
title = {A generalized Cauchy-Lipschitz theorem in low regularity spaces},
author = {Arnaud Heibig},
journal= {arXiv preprint arXiv:1701.02636},
year = {2017}
}