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Partial regularity of strong local minimizers of quasiconvex integrals with (p, q)-growth

Published online by Cambridge University Press:  26 May 2009

Sabine Schemm  and
Thomas Schmidt
Sabine Schemm
Affiliation:
Mathematisches Institut, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, 91054 Erlangen, Germany (schemm@mi.uni-erlangen.de)
Thomas Schmidt
Affiliation:
Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany (schmidt.th@uni-duesseldorf.de)
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Abstract

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We consider strictly quasiconvex integrals

in the multi-dimensional calculus of variations. For the C2-integrand f : ℝNn → ℝ we impose (p, q)-growth conditions

with γ, Γ > 0 and 1 < p ≤ q < min {p + 1/n, p(2n − 1)/(2n − 2)}. Under these assumptions we prove partial C1, αloc-regularity for strong local minimizers of F and the associated relaxed functional .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 3 , June 2009 , pp. 595 - 621
Copyright
Copyright © Royal Society of Edinburgh 2009