Electron. J. Diff. Eqns. Vol. 1995(1995), No. 06, pp. 1-14.

Regularity for Non-Uniformly Elliptic Systems and Application to Some Variational Integrals

F. Leonetti & C. Musciano

This paper deals with higher integrability for minimizers of some variational integrals whose Euler equation is elliptic but not uniformly elliptic. This setting is also referred to as elliptic equations with p,q-growth conditions, following Marcellini. Higher integrability of minimizers implies the existence of second derivatives. This improves on a result by Acerbi and Fusco concerning the estimate of the (possibly) singular set of minimizers.

Submitted September 20, 1994. Published June 7, 1995.
Math Subject Classification: 35J60, 49N60.
Key words: Regularity, weak solutions, minimizers, ellipticity, variational integrals.

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Francesco Leonetti
Dipartimento di Matematica, Universita di L'Aquila, Piazzale Aldo Moro 5, 00185 Roma, Italy
e-mail: leonetti@vxscaq.aquila.infn.it

Chiara Musciano
Istituto Nazionale di Alta Matematica Francesco Severi, Citt\`a Universitaria, Piazzale Aldo Moro 5, 00185 Roma, Italy

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