WAVELET SOLUTION TO THE THREE-DIMENSIONAL CAUCHY PROBLEM FOR LAPLACE EQUATION
Wang Jin-ru · Journal of Mathematics · 2012
We consider the three-dimensional Cauchy problem for the Laplace equation.The problem is ill-posed,its solution(if it exists) doesn't depend continuously on the initial data.Using Meyer wavelets and Galerkin method,we get stable wavelet approximate solutions.Furthermore,we shall give a recipe for choosing the coarse level resolution.