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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 2, 1998, pp. 393–415
DOI: 10.4171/ZAA/829

Published online: 1998-06-30

Variational Integrals on Orlicz-Sobolev Spaces

Martin Fuchs and V. Osmolovski[1]

(1) St. Petersburg State University, Russian Federation

We consider vector functions $u : \mathbb R^n \supset \Omega \to \mathbb R^N$ minimizing variational integrals of the form $\int_{\Omega} G(\triangledown u)dx$ with convex density $G$ whose growth properties are described in terms of an $N$-function $A : (0, \infty) \to (0, \infty)$ with limsup$_{t \to \infty} A(t)t^{–2} < \infty$. We then prove - under certain technical assumptions on $G$ - full regularity of $u$ provided that $n = 2$, and partial $C^1$-regularity in the case $n ≥ 3$. The main feature of the paper is that we do not require any power growth of $G$.

Keywords: Variational problems, minima, regularity theory, Orlicz-Sobolev spaces

Fuchs Martin, Osmolovski V.: Variational Integrals on Orlicz-Sobolev Spaces. Z. Anal. Anwend. 17 (1998), 393-415. doi: 10.4171/ZAA/829