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Polyconvexity

  • Filip RindlerEmail author
Chapter
  • 3.2k Downloads
Part of the Universitext book series (UTX)

Abstract

At the beginning of the previous chapter we saw that convexity cannot hold concurrently with frame-indifference (and a mild non-degeneracy condition). Thus, we were led to consider quasiconvex integrands. However, while quasiconvexity is of tremendous importance in the theory of the calculus of variations, our Lower Semicontinuity Theorem  5.16 has one major drawback: we needed to require the p-growth bound
$$ |f(x, A)| \le M(1+|A|^p), \qquad (x, A) \in \varOmega \times \mathbb {R}^{m \times d}, $$

Keywords

Quasiconvex Integrands Lower Semicontinuity Theorem Nonlinear Elasticity Theory Bounded Lipschitz Domain Polyconvex Integrands 
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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