Variational Integrals on Orlicz–Sobolev Spaces
Martin Fuchs
Universität des Saarlandes, Saarbrücken, GermanyV. Osmolovski
St. Petersburg State University, Russian Federation
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Abstract
We consider vector functions minimizing variational integrals of the form with convex density whose growth properties are described in terms of an -function with limsup. We then prove - under certain technical assumptions on - full regularity of provided that , and partial -regularity in the case . The main feature of the paper is that we do not require any power growth of .
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