Journal of Convex Analysis, Vol. 4, No. 2, pp. 289-303 (1997)

BMO Regularity for One-Dimensional Minimizers of some Lagrange Problems

Alberto Fiorenza

Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Universita di Napoli, Via Cintia, 80126 Napoli, Italy,

Abstract: We extend our results about a class of non-regular Lagrange problems of Calculus of Variations showing that the derivative of minimizers are in $BMO$. For this class we give also some results of optimality relative to the Tonelli set, of the type recently given by Ball-Mizel, by using results of Harmonic Analysis.

Keywords: Calculus of Variations, One-dimensional problems, Reverse Jensen Inequalities, Tonelli set, $BMO$, Orlicz Spaces

Classification (MSC2000): 49N60; 49K40, 46E30

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