Calculus of Variations and Partial Differential Equations

, Volume 29, Issue 1, pp 59–83

Direct approach to the problem of strong local minima in calculus of variations

Original Article

DOI: 10.1007/s00526-006-0056-7

Cite this article as:
Grabovsky, Y. & Mengesha, T. Calc. Var. (2007) 29: 59. doi:10.1007/s00526-006-0056-7


The paper introduces a general strategy for identifying strong local minimizers of variational functionals. It is based on the idea that any variation of the integral functional can be evaluated directly in terms of the appropriate parameterized measures. We demonstrate our approach on a problem of W1,∞ sequential weak-* local minima — a slight weakening of the classical notion of strong local minima. We obtain the first quasiconvexity-based set of sufficient conditions for W1,∞ sequential weak-* local minima.

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Temple UniversityPhiladelphiaUSA