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Convexity

  • Filip RindlerEmail author
Chapter
  • 3.3k Downloads
Part of the Universitext book series (UTX)

Abstract

In this chapter we start to develop the mathematical theory that will allow us to analyze the problems presented in the introduction, and many more. The basic minimization problem that we are considering is the following:
$$ \left\{ \begin{aligned}&\text {Minimize} \quad \mathscr {F}[u] := \int _\varOmega f(x, u(x), \nabla u(x)) \,\mathrm{d}x\\&\text {over all} \quad \quad u \in \mathrm {W}^{1,p}(\varOmega ;\mathbb {R}^m)\text { with }u|_{\partial \varOmega } = g. \end{aligned} \right. $$

Keywords

Basic Minimization Problem Legendre-Fenchel Duality Weak Lower Semicontinuity Weak Coercivity Rellich-Kondrachov Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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