Geodesic
Partial regularity of gradients of solutions for nonlinear nondiagonal systems in divergence form
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 20, Tome 171 (1989), pp. 66-69

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The partial $C^{1,\alpha}$-regularity of weak solutions for nonlinear parabolic nondiagonal systems in divergence form is proved. 
@article{ZNSL_1989_171_a4,
     author = {A. A. Zykov},
     title = {Partial regularity of gradients of solutions for nonlinear nondiagonal systems in divergence form},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--69},
     publisher = {mathdoc},
     volume = {171},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_171_a4/}
}
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A. A. Zykov. Partial regularity of gradients of solutions for nonlinear nondiagonal systems in divergence form. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 20, Tome 171 (1989), pp. 66-69. http://geodesic.mathdoc.fr/item/ZNSL_1989_171_a4/