Abstract
The numerical solution of the bi-dimensional nonlinear Poisson equations under Cauchy boundary conditions is considered. Using Green identity we show that this problem is equivalent to solve a bi-dimensional Fredholm integral equation of the first kind which can in turn be handled as a bi-dimensional generalized inverse moment problem. In the particular linear case the Helmholtz PDE is recovered and, within our scheme, the problem reduces to a bi-dimensional Hausdorff moment problem. In all the cases we find approximated solutions for the associated finite moment problems and bounds for the corresponding errors.
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