Regularity theorems for degenerate quasiconvex energies with (p,q)-growth - Schmidt, Thomas (Advances in Calculus of Variations, 2008)
We study autonomous integrals F[u]:=∫ Ω f(Du)dx for u: ℝ n ⊃ Ω.→ ℝ N in the multidimensional calculus of variations, where the integrand f is a strictly quasiconvex function satisfying the (p, q)-growth conditions γ|ξ| p ≤ f(ξ) ≤ Γ(1 + |ξ| q) with exponents 1< p≤ q < p + min2, p/2n, Imposing the additional assumption that f resembles the degenerate behavior of the p-energy density, we establish a partial C 1,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 f(ξ): = 1/p|ξ| p + h(det ξ), where h is a smooth convex function with q/n-growth. © de Gruyter 2008.
UnivIS-Import:2015-03-09:Pub.2008.nat.dma.lma2.regula_1
Keywords: Calculus of variations; Degeneration; Nonstandard growth; Partial regularity; Polyconvexity; Quasiconvexity; Relaxation