Regularity for some scalar variational problems under general growth conditions

  • P. Marcellini
Contributed Papers

DOI: 10.1007/BF02192251

Cite this article as:
Marcellini, P. J Optim Theory Appl (1996) 90: 161. doi:10.1007/BF02192251


We consider integrals of the calculus of variations over a set Ω of ℝn, and the related regularity result: are the minimizers smooth functions, say for example of classC(Ω)? Classically, the so-called natural growth conditions on the integrand have been the main sufficient assumptions for regularity. In recent years, motivated also by application, the interest in the study of this problem has increased under more general growth assumptions. In this paper, we propose some general growth conditions that guarantee regularity for a class of scalar variational problems.

Key Words

Calculus of variations direct methods regularity non-standard growth conditions general growth conditions 

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • P. Marcellini
    • 1
  1. 1.Department of Mathematics U. DiniUniversity of FlorenceFirenzeItaly

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