On the Existence of Solutions of Variational Inequalities in Nonreflexive Banach Spaces
We are concerned in this article with an existence theorem for variational inequalities in nonre exive Banach spaces with a general coercivity condition. The variational inequalities contain multivalued generalized pseudomonotone mappings and convex functionals, the nonre exive Banach spaces form a complementary system, and the coercivity condition involves both the mapping and the functional. As an application, we study second-order elliptic variational inequalities with multivalued lower-order terms in general Orlicz-Sobolev spaces.
V. K. Le, "On the Existence of Solutions of Variational Inequalities in Nonreflexive Banach Spaces," Banach Journal of Mathematical Analysis, vol. 13, no. 2, pp. 293-313, Tusi Mathematical Research Group (TMRG), Jan 2019.
The definitive version is available at https://doi.org/10.1215/17358787-2018-0034
Mathematics and Statistics
Keywords and Phrases
Multival- ued mapping; Nonre exive Banach space; Orlicz-Sobolev space; Variational inequality
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2019