Regularized Solution of the Initial Value Problem for the Laplace Equation Using Littlewood-Paley Wavelet
Xu Wang · Harbin Ligong Daxue xuebao · 2008
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.