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Non-Convex Integrands

  • Bernard Dacorogna
Part of the Applied Mathematical Sciences book series (AMS, volume 78)

Abstract

In Chapter 3 and 4 we have seen that in order to get existence theorems for
$$ \inf {\mkern 1mu} \{ {\mkern 1mu} I(u){\mkern 1mu} = {\mkern 1mu} \int\limits_\Omega {f(x,{\mkern 1mu} u(x),{\mkern 1mu} \nabla u(x)){\mkern 1mu} dx{\mkern 1mu} :{\mkern 1mu} u{\mkern 1mu} \in {\mkern 1mu} {u_0}{\mkern 1mu} + {\mkern 1mu} W_0^{1,p}(\Omega ;{\mathbb{R}^m})} \}$$
(1)
he convexity (or quasiconvexity in the vectorial case) of f, with respect to the last variable, plays a central role. In this chapter we shall study the case where f fails to be convex (quasiconvex in the vectorial case).

Keywords

Minimal Surface Existence Theorem Lower Semicontinuous Scalar Case Reverse Inequality 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Bernard Dacorogna
    • 1
  1. 1.Département de MathématiquesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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