Multi-Valued Variational Inequalities and Inclusions (Springer Monographs in Mathematics)

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Multi-Valued Variational Inequalities and Inclusions (Springer Monographs in Mathematics)

Carl, Siegfried/ Le, Vy Khoi

ウェブストア価格 ¥35,662（本体¥32,420）
Springer Nature Switzerland AG（2021/03発売）
外貨定価 US$ 169.99
ポイント 324pt

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製本 Hardcover:ハードカバー版／ページ数 584 p.
言語 ENG
商品コード 9783030651640

Full Description

This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces.

A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool forstudying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions.

This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.

- Introduction. - Mathematical Preliminaries. - Multi-Valued Variational Equations. - Multi-Valued Elliptic Variational Inequalities on Convex Sets. - Multi-Valued Parabolic Variational Inequalities on Convex Sets. - Multi-Valued Variational Inequalities in Unbounded Domains. - Multi-Valued Variational Inequalities with Convex Functionals.