Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth

Abstract

We prove a small excess regularity theorem for almost minimizers of a quasiconvex variational integral of subquadratic growth. The proof is direct, and it yields an optimal modulus of continuity for the derivative of the almost minimizer. The result is new for general almost minimizers, and in the case of absolute minimizers it considerably simplifies the existing proof. Mathematics Subject Classification (2000). 49N60, 26B25

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