Overview
- Develops a general sub-supersolution method for stationary and evolutionary multi-valued variational inequalities
- Provides a self-contained exposition of existence, comparison and enclosure principles
- Accessible to a wide audience of graduate students and researchers
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
Authors and Affiliations
About the authors
Siegfried Carl received his PhD in Mathematics from the University of Halle, where he has been a Professor of Mathematics at the Institute of Mathematics since 1995. He has published more than 150 research articles and three research monographs. He has served as an Associate Editor of various mathematical journals and acted as an Editor-in-Chief of the journal Nonlinear Analysis.
Vy Khoi Le received his PhD in Mathematics from the University of Utah, and has been a Professor of Mathematics at the Department of Mathematics and Statistics, Missouri University of Science and Technology since 2006. He is the author or co-author of more than 100 research articles and three research monographs. He has served as an Associate Editor of various international journals of mathematics.Bibliographic Information
Book Title: Multi-Valued Variational Inequalities and Inclusions
Authors: Siegfried Carl, Vy Khoi Le
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-65165-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-65164-0Published: 03 March 2021
Softcover ISBN: 978-3-030-65167-1Published: 04 March 2022
eBook ISBN: 978-3-030-65165-7Published: 02 March 2021
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XVII, 584
Number of Illustrations: 5 b/w illustrations
Topics: Analysis, Operator Theory, Optimization, Applications of Mathematics