Calculus of Variations and Geometric Measure Theory

E. Stepanov - D. Trevisan

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

created by stepanov on 10 Dec 2021
modified on 20 Oct 2022


Published Paper

Inserted: 10 dec 2021
Last Updated: 20 oct 2022

Journal: J. Differential Equations
Volume: 337
Pages: 91–137
Year: 2022


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\"{o}lder 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\"{o}lder continuous) functions; the solutions (integral manifolds) being also some very weakly regular geometric structures.

Keywords: Frobenius theorem, Rough paths, External differential systems, Young differential equations, Weak geometric structures