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We study the validity of an extension of Frobenius theorem on integralmanifolds for some classes of Pfaff-type systems of partial differentialequations involving multidimensional "rough" signals, i.e. "differentials" ofgiven H\"older continuous functions interpreted in a suitable way, similarly toYoung Differential Equations in Rough Paths theory. This can be seen as a toolto study solvability of exterior differential systems involving roughdifferential forms, i.e. the forms involving weak (distributional) derivativesof highly irregular (e.g. H\"older continuous) functions; the solutions(integral manifolds) being also some very weakly regular geometric structures.

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