Quasi-convex1ty and Lower Semi-continuity of Multiple Variational Integrals of Any Order

  title={Quasi-convex1ty and Lower Semi-continuity of Multiple Variational Integrals of Any Order},
  author={NORMAN G. MEYERS and N. G. MEYERS},
  • Published 2010
Here x = (x1, ■•-, x"),u = (u1, ■■-,u"'), Í2 is a bounded domain and the integrand fix,p°,---,p') is a continuous function of its arguments. In 1952 Morrey studied the case I = 1 and introduced the concept of quasiconvexity (see [3]). Extending this concept to the cases I = 1, we say that an integrand /(p') is quasi-convex if each polynomial of degree g / minimizes the integral, J"n/(D'n(x))dx, among all functions whose derivatives of order I—I satisfy a Lipschitz condition on Í2 (we denote… CONTINUE READING
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