Gradient Young measures generated by sequences in Sobolev spaces

  • David Kinderlehrer
  • Pablo Pedregal
Article

DOI: 10.1007/BF02921593

Cite this article as:
Kinderlehrer, D. & Pedregal, P. J Geom Anal (1994) 4: 59. doi:10.1007/BF02921593

Abstract

Oscillatory properties of a weak convergent sequence of functions bounded inLp, 1 ≤p ≤ ∞, may be summarized by the parametrized measure it generates. When such a measure is generated by the gradients of a sequence of functions bounded inH1,p, it must have special properties. The purpose of this paper is to characterize such parametrized measures as the ones that obey Jensen’s inequality for all quasiconvex functions with the appropriate growth at infinity. We have found subtle differences between the casesp < ∞ andp = ∞. A consequence is that any measure determined by biting convergence is in fact generated by a sequence convergent in a stronger sense. We also give a few applications.

Math Subject Classification

26B25 35J20 46E27 46E35 73C50 

Key Words and Phrases

Weak convergence “biting convergence,” lower semicontinuity Young measure calculus of variations 

Copyright information

© Mathematica Josephina, Inc. 1994

Authors and Affiliations

  • David Kinderlehrer
    • 1
    • 2
  • Pablo Pedregal
    • 1
    • 2
  1. 1.Department of Mathematics and Center for Nonlinear AnalysisCarnegie Mellon UniversityPittsburghUSA
  2. 2.Departamento de Matemática AplicadaUniversidad Complutense de MadridMadridSpain