ON THE CLASSICAL SOLUTION OF NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER
M. V. Safonov · Mathematics of the USSR-Izvestiya · 1989
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.