Some new results on differential inclusions for differential forms

Abstract

In this article we study some necessary and sufficient conditions for the existence of solutions in W 0 1 , ∞ ( Ω ; Λ k ) W_{0}^{1,\infty }(\Omega ;\Lambda ^{k}) of the differential inclusion \[ d ω ∈ E a.e. in  Ω d\omega \in E\quad \text {a.e. in }\Omega \] where E ⊂ Λ k + 1 E\subset \Lambda ^{k+1} is a prescribed set.