利用Littlewood-Paley小波讨论Laplace方程初值问题的正则解

Regularized Solution of the Initial Value Problem for the Laplace Equation Using Littlewood-Paley Wavelet

讨论了Laplace方程初值问题解的逼近.利用小波分析中的多分辨率分析方法,借助Littlewood-Paley小波在频域上的高频衰变性,把Laplace方程在边界条件下的解投影到紧支撑函数空间,来考虑Laplace方程初值问题的正则解.

This paper uses a multi-resolution analysis method in wavelet analysis, and through the quality that Littlewood-Paley wavelet decays with high-frequency in the frequency domain, considers the approximation of the solution of the Laplace equation＇ s initial value. Therefore, the paper projects the solution which is gained from the Laplace equation in boundary conditions to the space of compactly supported function, uses Littlewood-Paley wavelet＇ s compactly supported ability in the frequency domain, and further discusses the regularized solutions of the initial value of Laplace equation.