Regularity for non-unifomly elliptic systems and applications to some variational integrals

Abstract

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.

Keywords

• Regularity
• weak solutions
• minimizers
• ellipticity
• variational integrals.