Uniform Meyer Solution to the Three Dimensional Cauchy Problem for Laplace Equation
Year: 2011
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 3 : pp. 265–277
Abstract
We consider the three dimensional Cauchy problem for the Laplace equation$$\left\{\begin{array}{ll}u_{xx}(x,y, z)+u_{yy}(x,y, z)+u_{zz}(x,y, z) = 0, & x \in R, y \in R, 0 < z \leq 1,\\u(x,y,0) = g(x,y), & x \in R, y \in R,\\u_z(x,y,0) = 0, & x \in R, y \in R,\end{array}\right.$$where the data is given at $z = 0$ and a solution is sought in the region $x,y \in R$, $0 < z < 1$. The problem is ill-posed, the solution (if it exists) doesn’t depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.1007/s10496-011-0265-6
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 3 : pp. 265–277
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Laplace equation wavelet solution uniform convergence.