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关于一类抛物型Monge-Ampère方程解的注记
引用本文:陈丽,王光烈.关于一类抛物型Monge-Ampère方程解的注记[J].数学年刊A辑(中文版),2003(1).
作者姓名:陈丽  王光烈
作者单位:中国科学院数学与系统科学研究院,吉林大学数学研究所 北京 100080,长春 130023
基金项目:国家自然科学基金(No.1963150)资助的项目
摘    要:本文讨论如下抛物型Monge-Ampere方程的第一初边值问题-ut+det1/n D2u=g(χ,t),(χ,t)∈Q=Ω×(0,T),u= (χ,t),(χ,t)∈ pQ,其中Ω为Rn中有界凸集.证明了在更一般的结构条件下3,7]的结果仍然成立.证明中重要的一点是在Rn × R中非柱型域上“冻结问题”的可解性.

关 键 词:粘性解  非线性摄动  冻结问题

SOME REMARKS ON THE SOLUTION OF ONE TYPE OF PARABOLIC MONGE-AMPERE EQUATION
CHEN Li WANG GuanglieAcademy of Mathematics and System Sciences,CAS,Beijing ,China. E-mail: dongchli@mx.amss.ac.cnInstitute of Mathematics,Jilin University,Changchun ,China. E-mail: wanggl@mail.jlu.edu.cn.SOME REMARKS ON THE SOLUTION OF ONE TYPE OF PARABOLIC MONGE-AMPERE EQUATION[J].Chinese Annals of Mathematics,2003(1).
Authors:CHEN Li WANG GuanglieAcademy of Mathematics and System Sciences  CAS  Beijing  China E-mail: dongchli@mxamssaccnInstitute of Mathematics  Jilin University  Changchun  China E-mail: wanggl@mailjlueducn
Institution:CHEN Li WANG GuanglieAcademy of Mathematics and System Sciences,CAS,Beijing 100080,China. E-mail: dongchli@mx.amss.ac.cnInstitute of Mathematics,Jilin University,Changchun 130023,China. E-mail: wanggl@mail.jlu.edu.cn
Abstract:Some remarks are given on the results of 3] and 7]. The problem considered here is a bounded convex domain in R? It is obtained that the results in 3] and 7] are also true under a more general structure condition. One of the main points in the proof is the solvability of the "frozen problem" in a non-cylindrical domain in M?x R.
Keywords:Viscosity solution  Nonlinear perturbation  Frozen problem
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