Approximating the Solution to the Cauchy Problem and the Boundary Value for the Laplace Equation

In this paper it is proved that the Cauchy problem and a boundary value problem for the Laplace equation is well-posed provided the data belong to a suitable function space. Explicit numerical procedures are described for approximating the solutions to these problems. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.