Geodesic
The regularity of solutions of diagonal elliptic systems under boundary convex constraints
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 152 (1986), pp. 5-17

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We consider the variational inequalities connected with linear diagonal elliptic systems of the second order under boundary convex constraints. It is proved that the first derivatives of solutions are Holder continuous up to the boundary. 
@article{ZNSL_1986_152_a0,
     author = {A. A. Arkhipova and N. N. Ural'tseva},
     title = {The regularity of solutions of diagonal elliptic systems under boundary convex constraints},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--17},
     publisher = {mathdoc},
     volume = {152},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_152_a0/}
}
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A. A. Arkhipova; N. N. Ural'tseva. The regularity of solutions of diagonal elliptic systems under boundary convex constraints. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 152 (1986), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_1986_152_a0/