2021/12/10 by Eugene Stepanov, Stepanov, Eugene, Dario Trevisan +1
Engineering · #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2112.05565
openalex publication_date 2021/12/10 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
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 Hölder 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. Hölder continuous) functions; the solutions (integral manifolds) being also some very weakly regular geometric structures.