复变量Lewy方程的广义解和古典解

The generalized solution and classical solution of the complex variable Lewy equation

在广义函数空间讨论了复变量Lewy方程u/z-+iz(u/t)=1/2F(z,■,t)广义解的存在性,获得了广义解的表达式.Lewy方程u/z-+iz(u/t)=1/2f(t)当f(t)仅为连续函数时,此解还是在区域D内的古典解,且证明了存在f(t)∈C∞(R),但在区间[-T,+T]处处不解析,却有在R3的C∞解.

This issue we discussed the generalized solution of the complex variable Lewy equation au/az＋iz（au/at）=1/2F（z,z,t）.We have discussed the existence of the generalized solution of Lewy equation in the space of the generalized function and obtained the formula of the generalized solution. This solution is also the calssieal solution in the region of Dwhen F（z,z,t） = f（t） is a continuous function. And we have proved there exists f（t）∈C∞（R）isnot analytie everywhere,but have the solution C∞ at R3.