Multi-Valued Parabolic Variational Inequalities on Convex Sets

Author

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

Abstract

This chapter is devoted to multi-valued evolutionary variational inequalities of the abstract form and related systems under constraints given by closed convex sets K ⊂ L^p(0, τ;V ), where u′=du/dt denotes the generalized derivative of u: (0, τ) → V in the sense of vector space-valued distributions (see Chapter 2 ). It should be noted that unlike in the stationary case, in the treatment of its evolutionary counterpart (5.1) an additional difficulty arises. This difficulty is due to the appearance of the indicator function I_K representing the constraint, so that no growth condition can be assumed on ∂I_K, and therefore, in general, no estimate of the time derivative du/dt in the dual space L^p′(0, τ; V^∗) is available, which would be needed for proving existence of solutions.

Recommended Citation

S. Carl and V. K. Le, "Multi-Valued Parabolic Variational Inequalities on Convex Sets," Springer Monographs in Mathematics, pp. 287 - 354, Springer, Mar 2021.

The definitive version is available at https://doi.org/10.1007/978-3-030-65165-7_5

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