"On Variational Inequalities on Exterior Domains with Multivalued Conve" by Vy Khoi Le
 

On Variational Inequalities on Exterior Domains with Multivalued Convection Terms

Abstract

In this paper, we study variational inequalities of the form 〈−ΔNu,v−u〉+〈F(u),v−u〉≥0,∀v∈Ku∈K,where ΔNu=div|∇u|N−2∇u is the N-Laplacian, K is a closed convex set in the Beppo–Levi space X=D01,N(Ω), where Ω is the exterior of the closed unit ball B(0,1)¯ in RN (N≥2). We are interested here in the case where F is given by a multivalued function f=f(x,u,∇u) that depends also on the gradient ∇u of the unknown function. We consider a functional analytic framework of the above problem, including conditions on the lower order term f such that the problem can be appropriately formulated in X and a related weighted Orlicz space, and the involved mappings have certain useful monotonicity-continuity properties. Existence of solutions in coercive and noncoercive cases are studied. In the noncoercive case, we follow a sub-supersolution approach and prove the existence of solutions of the above inequality under a multivalued local growth condition of Bernstein–Nagumo type.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Convection Term; Multivalued Mapping; Pseudomonotone Mapping; Variational Inequality; Weighted Orlicz Space

International Standard Serial Number (ISSN)

1468-1218

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Elsevier, All rights reserved.

Publication Date

01 Apr 2023

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