Journal of Convex Analysis 11 (2004), No. 2, 437--476
Copyright Heldermann Verlag 2004
Partial and Full Boundary Regularity for Minimizers of Functionals with Nonquadratic Growth
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91094 Erlangen, Germany, firstname.lastname@example.org
Joseph F. Grotowski
Dept. of Mathematics, City College of New York, City University of New York, Convent Avenue at 138th Street, New York, NY 10031, U.S.A., email@example.com
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91094 Erlangen, Germany, firstname.lastname@example.org
We consider regularity at the boundary for minimizers of variational integrals whose integrands have nonquadratic growth in the gradient. Under relatively mild assumptions on the coefficients we obtain a partial regularity result. For coefficients of a more particular type, namely those satifying a particular splitting condition, we obtain full boundary regularity. The results are new for the situation under consideration. The key ingredients are a new version of the usual Gehring-type lemma, and a careful adaptation of the technique of dimension-reduction to the current setting.
MSC 2000: 49J45, 58E20.
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