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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
Frank Duzaar
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91094 Erlangen,
Germany, duzaar@mi.uni-erlangen.de
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.,
grotow@sci.ccny.cuny.edu
Manfred Kronz
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91094 Erlangen,
Germany, kronz@mi.uni-erlangen.de
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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