Geodesic
On the classical solution of nonlinear elliptic equations of second order
Izvestiya. Mathematics, Tome 33 (1989) no. 3, pp. 597-612 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Dirichlet problem $E(u_{x_ix_j},u_{x_i},u,x)=0$ in $\Omega\subset R^d$, $u=\varphi$ on $\partial\Omega$, is considered for nonlinear elliptic equations, including Bellman equations with “coefficients” in the Hölder space $C^{\alpha}(\overline\Omega)$. It is proved that if $\alpha>0$ is sufficiently small, then this problem is solvable in $C^{2+\alpha}_{\mathrm{loc}}(\Omega)\cap C(\overline\Omega)$. If in addition $\partial\Omega\in C^{2+\alpha}$ and $\varphi\in C^{2+\alpha}(\overline\Omega)$, then the solution belongs to $C^{2+\alpha}(\overline\Omega)$. Bibliography: 18 titles. 
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M. V. Safonov. On the classical solution of nonlinear elliptic equations of second order. Izvestiya. Mathematics, Tome 33 (1989) no. 3, pp. 597-612. http://geodesic.mathdoc.fr/item/IM2_1989_33_3_a6/

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