Multi-Valued Variational Inequalities in Unbounded Domains

Author

Siegfried Carl
Vy Khoi Le, Missouri University of Science and TechnologyFollow

Abstract

The main focus in this chapter is on multi-valued quasilinear elliptic variational inequalities of the form in all of ℝ^N as well as in the exterior domain Ω = ℝ^N ∖ B̅(0̅,1̅ ), where only for simplifying our presentation A: X → X^∗ is given by the p-Laplacian, that is, A = − Δ_p, see Section 6.3. The study of elliptic equations in unbounded domains and even more the study of multi-valued quasilinear elliptic variational inequalities in unbounded domains causes a number of additional difficulties, and therefore cannot be considered as just a straightforward extension of the bounded domain problems. That is why the multi-valued lower order term ℱ_a is of the form ℱ_a= aℱ(u) with a: ℝ^N→ ℝ (resp. a: Ω → ℝ ) satisfying a certain decay property at infinity.

Recommended Citation

S. Carl and V. K. Le, "Multi-Valued Variational Inequalities in Unbounded Domains," Springer Monographs in Mathematics, pp. 355 - 464, Springer, Mar 2021.

The definitive version is available at https://doi.org/10.1007/978-3-030-65165-7_6

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

1439-7382

Document Type

Book - Chapter

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Springer, All rights reserved.

Publication Date

03 Mar 2021