An existence theorem for non-homogeneous differential inclusions in Sobolev spaces

Jean Philippe Mandallena, Mikhail Sychev

Research output: Contribution to journalArticlepeer-review

Abstract

In the present paper, we establish an existence theorem for non-homogeneous differential inclusions in Sobolev spaces. This theorem extends the results of Müller and Sychev [S. Müller and M. A. Sychev, Optimal existence theorems for nonhomogeneous differential inclusions, J. Funct. Anal. 181 2001, 2, 447-475; M. A. Sychev, Comparing various methods of resolving differential inclusions, J. Convex Anal. 18 2011, 4, 1025-1045] obtained in the setting of Lipschitz functions. We also show that solutions can be selected with the property of higher regularity.

Original languageEnglish
JournalAdvances in Calculus of Variations
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Baire category
  • convex integration
  • higher regularity
  • ind functional
  • Non-homogeneous differential inclusions
  • sequences obtained by perturbation

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