Geodesic
Partial applicability of Moser's method to nonlinear elliptic systems
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 547-557

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We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutions $u\in W_p^1$. It is proved that $Du\in L_q$ with some $q\in(p;+\infty)$ and it is explicitly shown how $q$ depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds. 
@article{MZM_1995_58_4_a6,
     author = {E. A. Kalita},
     title = {Partial applicability of {Moser's} method to nonlinear elliptic systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {547--557},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a6/}
}
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E. A. Kalita. Partial applicability of Moser's method to nonlinear elliptic systems. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 547-557. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a6/