|
|
| |
| AN IMPROVEMENT OF A RESULT OF IVOCHKINA AND LADYZHENSKAYA ON A TYPE OF PARABOLIC MONGE-AMP\`ERE EQUATION |
| |
Citation： |
Wang Rouhuai,Wang Guangli.AN IMPROVEMENT OF A RESULT OF IVOCHKINA AND LADYZHENSKAYA ON A TYPE OF PARABOLIC MONGE-AMP\`ERE EQUATION[J].Chinese Annals of Mathematics B,1997,18(4):405~422 |
| Page view： 1222
Net amount： 761 |
Authors： |
Wang Rouhuai; Wang Guangli |
Foundation： |
the National Natural Science Foundation of China |
|
|
| 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. |
Keywords： |
Nonlinear perturbation, Less regularity about data, Interior regularity of viscosity solutions |
Classification： |
35K20, 35K55, 35Q99 |
|
|
Download PDF Full-Text
|
|
|
|
