Multi-Valued Variational Inequalities with Convex Functionals
In this chapter, the sub-supersolution method is extended to MVIs (1.1 ) and (1.3 ) with general convex, lower semicontinuous, and proper functionals Ψ. The convex functionals are seen here as characterizations of various constraints imposed on the problems, as well as potential functionals of possibly multi-valued leading operators. Compared to the case of MVIs on closed and convex sets, this more general situation is not a direct extension and requires the introduction of new concepts and implementation of new techniques in both classes of stationary and evolutionary MVIs. In this chapter, we also investigate stationary MVIs, formulated in Sobolev spaces with variable exponents, in which the lower order terms may depend on both the unknown function u and its gradient ∇u.
S. Carl and V. K. Le, "Multi-Valued Variational Inequalities with Convex Functionals," Springer Monographs in Mathematics, pp. 465-569, Springer, Mar 2021.
The definitive version is available at https://doi.org/10.1007/978-3-030-65165-7_7
Mathematics and Statistics
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03 Mar 2021