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New regularity theorems for non-autonomous variational integrals with (p, q)-growth

  • Dominic BreitEmail author
Article

Abstract

One prominent problem in the calculus of variations is minimizing anisotropic integrals with a (p, q)-elliptic density F depending on the gradient of a function \({w : \Omega \rightarrow \mathbb{R}^N}\) with \({\Omega \subset \mathbb{R}^n}\) . The best known sufficient bound for regularity of solutions is qp (n + 2)/n. On the other hand, if we allow an additional x-dependence of the density we have the much weaker result qp (n + 1)/n. If one additionally imposes the local boundedness of the minimizer, then these bounds can be improved to qp + 2 and qp + 1. In this paper we give natural assumptions for F closing the gap between the autonomous and non-autonomous situation.

Mathematics Subject Classification (2000)

49 N 60 49 N 99 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsSaarland UniversitySaarbrückenGermany

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