An existence theorem for non-homogeneous differential inclusions in Sobolev spaces-Reference-Cited by-同舟云学术

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

Published:2019-07-12 Issue:3 Volume:14 Page:313-326
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Mandallena Jean-Philippe¹,Sychev Mikhail²

Affiliation:

1. Laboratoire MIPA , Université de Nîmes , Site des Carmes, Place Gabriel Péri, 30021 Nîmes , France

2. Laboratory of Differential Equations and Related Problems in Analysis , Sobolev Institute of Mathematics , Koptuyg Avenue 4 , Novosibirsk 630090; and Novosibirsk State University , Russia

Abstract

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.

Funder

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2018-0076/pdf

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