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

AbstractWe consider almost respectively strong almost minimizers to quasi-convex variational integrals. Under a polynomial growth condition on the integrand and conditions on the function ω determing the almost minimality, in particular the assumption that Ω(r)=∫0rω(ρ)ρ−1dρ is finite for some r>0, we establish almost everywhere C1-regularity for almost minimizers. Under the weaker assumption that ω is bounded and limρ↓0ω(ρ)=0 we prove almost everywhere C0,α-regularity for strong almost minimizers to quasi-convex variational integrals of quadratic growth