Smoothness of radial solutions to Monge-Ampère equations
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چکیده
are smooth, given that k is smooth and nonnegative. When u is radial, (1) reduces to a nonlinear ODE on [0, 1) that is singular at the endpoint 0. It is thus easy to prove that u is always smooth away from the origin, even where k vanishes, but smoothness at the origin is more complicated, and determined by the order of vanishing of k there. In fact, Monn [9] proves that if k = k (x) is independent of u and Du, then a radial solution u to (1) is smooth if k 1 n is smooth, and Derridj [4] has extended
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تاریخ انتشار 2008