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Article Dans Une Revue Advances in Calculus of Variation Année : 2021

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

Résumé

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.
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Dates et versions

hal-03348501 , version 1 (19-09-2021)

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Jean-Philippe Mandallena, Mikhail Sychev. An existence theorem for non-homogeneous differential inclusions in Sobolev spaces. Advances in Calculus of Variation, 2021, 14 (3), pp.313-326. ⟨10.1515/acv-2018-0076⟩. ⟨hal-03348501⟩

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