Regularity theorems for degenerate quasiconvex energies with (p,q)-growth
Schmidt T (2008)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2008
Journal
Publisher: Walter de Gruyter
Book Volume: 1
Pages Range: 241-270
Journal Issue: 3
URI: http://cvgmt.sns.it/paper/1764/
DOI: 10.1515/ACV.2008.010
Abstract
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 + min{2, 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.
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How to cite
APA:
Schmidt, T. (2008). Regularity theorems for degenerate quasiconvex energies with (p,q)-growth. Advances in Calculus of Variations, 1(3), 241-270. https://dx.doi.org/10.1515/ACV.2008.010
MLA:
Schmidt, Thomas. "Regularity theorems for degenerate quasiconvex energies with (p,q)-growth." Advances in Calculus of Variations 1.3 (2008): 241-270.
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