Geodesic
On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case)
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 5-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a class of strong-nonlinear elliptic systems with a nondiagonal principal matrix. Weak solvability of the Dirichlet problem for such type systems was earlier proved by the author in the two-dimensional case. The solution constructed was smooth almost everywhere. Here we prove that this solution is a Hölder continuous function in the entire domain. 
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     author = {A. A. Arkhipova},
     title = {On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case)},
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A. A. Arkhipova. On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case). Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 5-13. http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a0/

[1] A. Arkhipova, “Solvability problem for nondiagonal elliptic systems with quadratic nonlinearity in the gradient (the two-dimensional case)”, Zap. Nauchn. Semin. POMI, 295, 2003, 5–17 | MR | Zbl

[2] A. Arkhipova, “Quasireverse Hölder inequalities and a priori estimates for quasilinear elliptic systems”, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 14 (2003), 91–108 | MR | Zbl

[3] J. Freshe, “On two-dimensional quasilinear elliptic systems”, Manuscr. Math., 28 (1979), 21–50 | DOI | MR