Geodesic
Partial regularity up to the boundary of weak solutions of elliptic systems with nonlinearity $\bold q$ greater than two
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Tome 271 (2000), pp. 63-82 
A. A. Arkhipova. Partial regularity up to the boundary of weak solutions of elliptic systems with nonlinearity $\bold q$ greater than two. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Tome 271 (2000), pp. 63-82. http://geodesic.mathdoc.fr/item/ZNSL_2000_271_a4/
@article{ZNSL_2000_271_a4,
     author = {A. A. Arkhipova},
     title = {Partial regularity up to the boundary of weak solutions of elliptic systems with nonlinearity $\bold q$~greater than two},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {63--82},
     year = {2000},
     volume = {271},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_271_a4/}
}
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Nonlinear elliptic systems with q-growth are considered. It is assumed that additional nonlinear terms of the systems have $q$-growth in the gradient, $q>2$. For Dirichlet and Neumann boundary-value problems we study the regularity of weak bounded solutions in the vicinity of the boundary. In the case of small dimensions $(n\le q+2)$, the Hölder continuity or partial Hölder continuity of the solutions up to the boundary is proved. In a previous article the author studied the same problem for $q=2$.