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Some new results on differential inclusions for differential forms


Authors: Saugata Bandyopadhyay, Bernard Dacorogna and Olivier Kneuss
Journal: Trans. Amer. Math. Soc. 367 (2015), 3119-3138
MSC (2010): Primary 35F60
DOI: https://doi.org/10.1090/S0002-9947-2014-06014-5
Published electronically: December 3, 2014
MathSciNet review: 3314803
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Abstract | References | Similar Articles | Additional Information

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

$\displaystyle d\omega \in E$$\displaystyle \quad \text {a.e. in }\Omega $

where $ E\subset \Lambda ^{k+1}$ is a prescribed set.

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Additional Information

Saugata Bandyopadhyay
Affiliation: Department of Mathematics & Statistics, Indian Institutes of Science Education and Research, Kolkata, India
Email: saugata.bandyopadhyay@gmail.com

Bernard Dacorogna
Affiliation: Section de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Email: bernard.dacorogna@epfl.ch

Olivier Kneuss
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Address at time of publication: Department of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
Email: olivier.kneuss@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2014-06014-5
Received by editor(s): July 24, 2012
Received by editor(s) in revised form: November 5, 2012
Published electronically: December 3, 2014
Additional Notes: Part of the present work was done while the first and third authors were visiting EPFL, whose hospitality is gratefully acknowledged
Article copyright: © Copyright 2014 American Mathematical Society