TY  - GEN
T1  - Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals
A1  - Bildhauer,Michael
A1  - Fuchs,Martin
Y1  - 2012/03/13
N2  - We consider local minimizers u:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{N} of variational integrals I[u]:=\int_{\Omega}F(\nabla u)dx, where F is of anisotropic (p,q)-growth with exponents 1<p\leq q<\infty. If F is in a certain sense decomposable, we show that the dimensionless restriction q\leq2p+2 together with the local boundedness of u implies local integrability of \nabla u for all exponents t\leq p+2. More precisely, the initial exponents for the integrability of the partial derivatives can be increased by two, at least locally. If n = 2, then we use these facts to prove C^{1,\alpha}-regularity of u for any exponents 2\leq p\leq q.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4673
ER  -