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Regularity results for local minimizers of energies with general densities having superquadratic growth


Author: M. Fuchs
Original publication: Algebra i Analiz, tom 21 (2009), nomer 5.
Journal: St. Petersburg Math. J. 21 (2010), 825-838
MSC (2010): Primary 49N60
DOI: https://doi.org/10.1090/S1061-0022-2010-01120-8
Published electronically: July 15, 2010
MathSciNet review: 2604569
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Abstract: Variational integrals whose energy densities are represented by $ N$- functions $ h$ of at least quadratic growth are considered. Under rather general conditions on $ h$, almost everywhere regularity of vector-valued local minimizers is established, and it is possible to include the case of higher order variational problems without essential changes in the arguments.


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Additional Information

M. Fuchs
Affiliation: Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, D–66041 Saarbrücken, Germany
Email: fuchs@math.uni-sb.de

DOI: https://doi.org/10.1090/S1061-0022-2010-01120-8
Keywords: Vector-valued problems, local minimizers, nonstandard growth, partial regularity
Received by editor(s): August 8, 2008
Published electronically: July 15, 2010
Article copyright: © Copyright 2010 American Mathematical Society

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