Geodesic
Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System
Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 89-97

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We study the complete regularity of the solutions of a nondiagonal elliptic system of nonlinear differential equations of divergent form whose coefficients are sufficiently slowly varying functions of their arguments and whose off-diagonal terms are sufficiently small. To this end, we apply a technique based on successive approximations to the solution and the use of Schauder estimates at each step.
Keywords: nonlinear differential equation, elliptic system, Schauder estimate, complete regularity of solutions, Dirichlet boundary condition, Hölder continuity. 
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     author = {D. V. Portnyagin},
     title = {Schauder {Estimates} and {Complete} {Regularity} of the {Solutions} of an {Elliptic} {System}},
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D. V. Portnyagin. Schauder Estimates and Complete Regularity of the Solutions of an Elliptic System. Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 89-97. http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a7/