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Abstract
We study autonomous integrals
F[u] := ∫Ω ƒ(Du) dx for u : ℝn ⊃ Ω → ℝN
in the multidimensional calculus of variations, where the integrand ƒ is a strictly quasiconvex function satisfying the (p, q)-growth conditions
γ|ξ|p ≤ ƒ(ξ) ≤ Γ(1 + |ξ|q)
with exponents 
. Imposing the additional assumption that ƒ resembles the degenerate behavior of the p-energy density, we establish a partial C1,α-regularity theorem for F-minimizers and a similar theorem for minimizers of a relaxed functional.
Our results cover the model case of polyconvex integrands
,
where h is a smooth convex function with 
-growth
Keywords.: Calculus of variations; partial regularity; quasiconvexity; polyconvexity; nonstandard growth; degeneration; relaxation
Received: 2007-08-09
Revised: 2008-04-30
Published Online: 2008-11-25
Published in Print: 2008-October
© de Gruyter 2008
