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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 3119-3138
  • MSC (2010): Primary 35F60
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06014-5
  • MathSciNet review: 3314803