Geodesic
Partial and Full Boundary Regularity for Minimizers of Functionals with Nonquadratic Growth
Journal of convex analysis, Tome 11 (2004) no. 2, pp. 437-476
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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. 
@article{JCA_2004_11_2_JCA_2004_11_2_a10,
     author = {F. Duzaar and J. F. Grotowski and M. Kronz},
     title = {Partial and {Full} {Boundary} {Regularity} for {Minimizers} of {Functionals} with {Nonquadratic} {Growth}},
     journal = {Journal of convex analysis},
     pages = {437--476},
     year = {2004},
     volume = {11},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a10/}
}
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F. Duzaar; J. F. Grotowski; M. Kronz. Partial and Full Boundary Regularity for Minimizers of Functionals with Nonquadratic Growth. Journal of convex analysis, Tome 11 (2004) no. 2, pp. 437-476. http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a10/