Variational Integrals on Orlicz-Sobolev Spaces

  • Martin Fuchs

    Universität des Saarlandes, Saarbrücken, Germany
  • V. Osmolovski

    St. Petersburg State University, Russian Federation


We consider vector functions u:RnΩRNu : \mathbb R^n \supset \Omega \to \mathbb R^N minimizing variational integrals of the form ΩG(u)dx\int_{\Omega} G(\triangledown u)dx with convex density GG whose growth properties are described in terms of an NN-function A:(0,)(0,)A : (0, \infty) \to (0, \infty) with limsuptA(t)t2<_{t \to \infty} A(t)t^{–2} < \infty. We then prove - under certain technical assumptions on GG - full regularity of uu provided that n=2n = 2, and partial C1C^1-regularity in the case n3n ≥ 3. The main feature of the paper is that we do not require any power growth of GG.

Cite this article

Martin Fuchs, V. Osmolovski, Variational Integrals on Orlicz-Sobolev Spaces. Z. Anal. Anwend. 17 (1998), no. 2, pp. 393–415

DOI 10.4171/ZAA/829