A Priori Limitations for Solutions of Monge-ampere Equations. Ii* By
نویسنده
چکیده
In this paper we are concerned with the convergence of solutions of elliptic and analytic Monge-Ampère equations. Theorem 1 gives the principal result of this paper. The example on p.^372 indicates the possibility of certain types of singularities which for linear elliptic equations cannot occur. Theorems 2 and 3 give sufficient conditions for the analyticity of the limit function. These conditions allow applications to certain probTems of the differential geometry in the large. Our method consists in introducing a regularizing contact transformation which transforms convex functions into functions with bounded second derivatives and thus makes possible the reduction of Theorem 1 to the principal result of the first part of this paper. 1. Regularizing contact transformation. Consider the contact transformation T of an (x, y, z)-space into a (£, r¡, f)-space generated by the relation
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