On exterior differential systems involving differentials of H\"{o}lder functions
Analysis of PDEs
2021-12-13 v1
Abstract
We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional "rough" signals, i.e. "differentials" of given H\"older continuous functions interpreted in a suitable way, similarly to Young Differential Equations in Rough Paths theory. This can be seen as a tool to study solvability of exterior differential systems involving rough differential forms, i.e. the forms involving weak (distributional) derivatives of highly irregular (e.g. H\"older continuous) functions; the solutions (integral manifolds) being also some very weakly regular geometric structures.
Keywords
Cite
@article{arxiv.2112.05565,
title = {On exterior differential systems involving differentials of H\"{o}lder functions},
author = {Eugene Stepanov and Dario Trevisan},
journal= {arXiv preprint arXiv:2112.05565},
year = {2021}
}