Nonsmooth Variational Problems and Their Inequalities

Comparison Principles and Applications

  • Siegfried Carl
  • Vy Le Khoi
  • Dumitru Motreanu

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Pages 1-10
  3. Pages 81-142
  4. Pages 211-278
  5. Back Matter
    Pages 379-395

About this book


This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems.

The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained.

This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers.


Boundary value problem Mathematica differential equation functional analysis partial differential equation

Authors and affiliations

  • Siegfried Carl
    • 1
  • Vy Le Khoi
    • 2
  • Dumitru Motreanu
    • 3
  1. 1.Institut für MathematikMartin-Luther-Universität Halle-WittenbergHalleGermany
  2. 2.Department of Mathematics and StatisticsUniversity of Missouri-RollaRollaUSA
  3. 3.Département de MathématiquesUniversité de PerpignanPerpignanFrance

Bibliographic information

Industry Sectors
Finance, Business & Banking