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A Comparison Principle for Parabolic Complex Monge–Ampère Equations
The Journal of Geometric Analysis ( IF 1.1 ) Pub Date : 2021-12-02 , DOI: 10.1007/s12220-021-00748-4 Hoang-Son Do 1 , Thanh Cong Ngoc Pham 2
中文翻译:
抛物线复数 Monge-Ampère 方程的比较原理
更新日期:2021-12-04
The Journal of Geometric Analysis ( IF 1.1 ) Pub Date : 2021-12-02 , DOI: 10.1007/s12220-021-00748-4 Hoang-Son Do 1 , Thanh Cong Ngoc Pham 2
Affiliation
In this paper, we study the Cauchy–Dirichlet problem for parabolic complex Monge–Ampère equations on strongly pseudoconvex domains using the viscosity method. We prove a comparison principle for parabolic complex Monge–Ampère equations and use it to study the existence and uniqueness of viscosity solution in certain cases where the sets \(\{z\in \Omega : f(t, z)=0 \}\) may be pairwise disjoint.
中文翻译:
抛物线复数 Monge-Ampère 方程的比较原理
在本文中,我们使用粘度方法研究了强伪凸域上抛物线复 Monge-Ampère 方程的 Cauchy-Dirichlet 问题。我们证明了抛物线复 Monge-Ampère 方程的比较原理,并用它来研究在集合\(\{z\in \Omega : f(t, z)=0 \} 的某些情况下粘度解的存在性和唯一性\)可能是成对不相交的。