Abstract
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.
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Marcellini, P. Regularity for some scalar variational problems under general growth conditions. J Optim Theory Appl 90, 161–181 (1996). https://doi.org/10.1007/BF02192251
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DOI: https://doi.org/10.1007/BF02192251