Archive for Rational Mechanics and Analysis

, Volume 95, Issue 3, pp 227–252

Quasiconvexity and partial regularity in the calculus of variations

  • Lawrence C. Evans

DOI: 10.1007/BF00251360

Cite this article as:
Evans, L.C. Arch. Rational Mech. Anal. (1986) 95: 227. doi:10.1007/BF00251360


We prove partial regularity of minimizers of certain functionals in the calculus of variations, under the principal assumption that the integrands be uniformly strictly quasiconvex. This is of interest since quasiconvexity is known in many circumstances to be necessary and sufficient for the weak sequential lower semicontinuity of these functionals on appropriate Sobolev spaces. Examples covered by the regularity theory include functionals with integrands which are convex in the determinants of various submatrices of the gradient matrix.

Copyright information

© Springer-Verlag GmbH & Co 1986

Authors and Affiliations

  • Lawrence C. Evans
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege Park