Some new results on differential inclusions for differential forms

Bandyopadhyay, Saugata; Dacorogna, Bernard; Kneuss, Olivier

doi:10.1090/S0002-9947-2014-06014-5

Some new results on differential inclusions for differential forms
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by Saugata Bandyopadhyay, Bernard Dacorogna and Olivier Kneuss PDF

Trans. Amer. Math. Soc. 367 (2015), 3119-3138 Request permission

Abstract:

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

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