The Dirichlet problem in , on , is considered for nonlinear elliptic equations, including Bellman equations with coefficients in the Holder space . It is proved that if 0$ SRC=http://ej.iop.org/images/0025-5726/33/3/A07/tex_im_858_img6.gif/> is sufficiently small, then this problem is solvable in . If in addition and , then the solution belongs to . Bibliography: 18 titles.
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M. V. Safonov (1989) studied this question.
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