TY - GEN T1 - Interior regularity for free and constrained local minimizers of variational integrals under general growth and ellipticity conditions A1 - Bildhauer,Michael A1 - Fuchs,Martin Y1 - 2011/12/01 N2 - We consider strictly convex energy densities f:\mathbb{R}^{n}\rightarrow\mathbb{R} under nonstandard growth conditions. More precisely, we assume that for some constants \lambda, \Lambda and for all Z,Y\in\mathbb{R}^{n} the inequality \lambda(1+\left|Z\right|^{2})^{-\frac{\mu}{2}}\left|Y\right|^{2}\leq D^{2}f(Z)(Y,Y)\leq\Lambda(1+\left|Z\right|^{2})^{\frac{q-2}{2}}\left|Y\right|^{2} holds with exponents \mu\in\mathbb{R} and q>1. If u denotes a bounded local minimizer of the energy \int f(\nabla w)dx subject to a constraint of the form w\geq\psi a.e. with a given obstacle \psi\in C^{1,\alpha}(\Omega), then we prove local C^{1,\alpha}-regularity of u provided that q<4-\mu. This result substantially improves what is known up to now (see, for instance, [CH], [BFM], [FM]), even for the case of unconstrained local minimizers. CY - Saarbrücken PB - Universitäts- und Landesbibliothek AD - Postfach 151141, 66041 Saarbrücken UR - http://scidok.sulb.uni-saarland.de/volltexte/2011/4377 ER -