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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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.
Si dimostra un risultato di regolarità parziale globale per le soluzioni deboli del problema di Dirichlet associato al sistema superellittico non lineare $\operatorname{div} A(x,u,Du) + B(x, u, DU) = 0$ con ipotesi di crescita naturale polinomiale delle funzioni coefficienti $A$ e $B$. Si applica il metodo indiretto della forma bilineare e non si fa uso di una diseguaglianza di Caccioppoli né di una diseguaglianza di Hölder al contrario. 
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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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