The first initial-boundary value problem for fully nonlinear parabolic equations generated by functions of the eigenvalues of the Hessian

For a class of elliptic Hessian operators raised by Caffarelli–Nirenberg–Spruck, the corresponding parabolic Monge–Ampère equation was studied, the existence and uniqueness of the admissible solution to the first initial-boundary value problem for the equation were established, which extended a result of Ivochkina–Ladyzhenskaya. © 2007 Elsevier Inc. All rights reserved.