| Abstract: | For the initial-boundary value problem about a type of parabolic Monge-Amp\'ere equation of the form (IBVP):
$\{-D_tu+(\det D^2_xu)^{1/n}=f(x,t),(x,t)\in Q=\Omega\times(0,T], u(x,t)=\phi(x,t)(x,t)\in\partial_pQ
\},$ where $\Omega$ is a bounded convex domain in $\bold R^n$,
the result in 4] by Ivochkina and Ladyzheskaya is improved in the sense that, under assumptions that the data of the problem possess lower regularity and satisfy lower order compatibility conditions than those in 4], the existence of classical solution to (IBVP) is still established (see Theorem 1.1 below). This can not be realized by only using the method in 4]. The main additional effort the authors have done
is a kind of nonlinear perturbation. |
