JournalsaihpcVol. 28, No. 3pp. 395–411

Higher differentiability of minimizers of convex variational integrals

  • Menita Carozza

    Università del Sannio, Piazza Arechi II – Palazzo De Simone, 82100 Benevento, Italy

  • Jan Kristensen

    Mathematical Institute, University of Oxford, 24-29 St. Gilesʼ, Oxford OX1 3LB, England, United Kingdom

  • Antonia Passarelli di Napoli

    Università di Napoli ‘Federico’, Dipartimento di Mat. e Appl. ‘R. Caccioppoli’, Via Cintia, 80126 Napoli, Italy
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Abstract

In this paper we consider integral functionals of the form

with convex integrand satisfying growth conditions. We prove local higher differentiability results for bounded minimizers of the functional under dimension-free conditions on the gap between the growth and the coercivity exponents.

As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand.

Cite this article

Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli, Higher differentiability of minimizers of convex variational integrals. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 3, pp. 395–411

DOI 10.1016/J.ANIHPC.2011.02.005