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本文讨论反射天线面设计中出现的一个偏微分方程,这是一个完全非线性Monge-Ampère型方程.我们先给出一个广义解的定义,然后介绍如何得到广义解的存在性、唯一性和正则性,最后我们给出求数值解的一个方法.
This article discusses a partial differential equation appearing in the design of a reflector antenna, which is a completely nonlinear Monge-Ampère type equation. We first give a definition of generalized solutions and then introduce how to obtain the existence, uniqueness and regularity of generalized solutions Finally, we give a way to solve numerical solutions.