Geodesic
Partial Boundary Regularity of Solutions of Nonlinear Superelliptic Systems
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 63-81

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Zbl MR
We prove global partial regularity of weaksolutions of the Dirichlet problem for the nonlinear superelliptic system $\operatorname{div} A(x,u,Du)+B(x, u, DU) = 0$, under natural polynomial growth of the coefficient functions $A$ and $B$. We employ the indirect method of the bilinear form and do not use a Caccioppoli or a reverse Hölder inequality. 
Hamburger, Christoph. Partial Boundary Regularity of Solutions of Nonlinear Superelliptic Systems. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 63-81. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a3/
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     title = {Partial {Boundary} {Regularity} of {Solutions} of {Nonlinear} {Superelliptic} {Systems}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {63--81},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {1},
     zbl = {1178.35178},
     mrnumber = {2310958},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a3/}
}
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