Geodesic
Partial regularity for quasilinear nonuniformly elliptic systems of the total type
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 62-70 
A. V. Ivanov; M. Frasca. Partial regularity for quasilinear nonuniformly elliptic systems of the total type. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 62-70. http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a5/
@article{ZNSL_1992_200_a5,
     author = {A. V. Ivanov and M. Frasca},
     title = {Partial regularity for quasilinear nonuniformly elliptic systems of the total type},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {62--70},
     year = {1992},
     volume = {200},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We establish partial $C^{1,\alpha}$-regularity of weak solutions of nonhomogeneous nondiagonal nonuniformly elliptic systems of the type $$ -\partial/\partial x_\alpha A^i_\alpha(x,u,u_x)=B^i(x,u,u_x),\quad i=1,\dots,N. $$ The typical example of admissible systems is the system of the Euler equations of the variational problem on a minimum of integral $\int_\Omega\mathcal{F}(u_x)d\,x$ with the integrand of the type $$ \mathcal{F}(p)=a|p|^2+b|p|^m+\sqrt{1+\mathrm{det}^2p},\quad a>0,\ b>0, $$ if $b$ is sufficiently large.