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arXiv · 2112.05565

On exterior differential systems involving differentials of H\"{o}lder functions

Eugene Stepanov·Dario Trevisan
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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.

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Eugene Stepanov, Dario Trevisan. 2021-12-10. On exterior differential systems involving differentials of H\"{o}lder functions. https://arxiv.org/abs/2112.05565

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