Some fully non-linear parabolic partial differential equations

Abstract

In this paper I wish to discuss the classical solvability of the first boundary value problem for a class of non-linear parabolic equations of second order. The equations to be considered arise from symmetric functions in a natural way analagous to the equations considered by Caffarelli, Nirenberg and Spruck [CNS] in the elliptic case. They are also motivated by the proposed analogue of the Monge-Ampère equation of Krylov [KL which is considered here as a first special case. I do not present the proofs of the results described, but only rough indications of the methods involved. The work constitutes the central results of the latter half of my doctoral dissertation [R l]