Regularity of ω-minimizers of quasi-convex variational integrals with polynomial growth

We consider almost respectively strong almost minimizers to quasi-convex variational integrals. Under a polynomial growth condition on the integrand and conditions on the function omega determing the almost minimality, in particular the assumption that Omega (r) = integral(0)(r) rootomega(rho)rho (-1) drho is finite for some r > 0, we establish almost everywhere C-1-regularity for almost minimizers. Under the weaker assumption that omega is bounded and lim(rhodown arrow0)omega(rho) = 0 we prove almost everywhere C-0,C-alpha-regularity for strong almost minimizers to quasi-convex variational integrals of quadratic growth. (C) 2002 Elsevier Science B.V. All rights reserved.