### Solution of an equation in Poisson partial derivatives with conditions of Dirichlet using techniques of the inverse moments problem

#### Abstract

In this paper, it will be shown that finding solutions from the Helmholtz equation and the non-linear Poisson equation under Dirichlet conditions is equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular in principle. We will see that an approximate solution of the equation in partial derivatives can be found using the techniques of generalized inverse moments problem and bounds for the error of the estimated solution. The method consists of two steps.In each one an integral equation is solved numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.

**How to Cite this Article:**Maria B. Pintarelli, Solution of an equation in Poisson partial derivatives with conditions of Dirichlet using techniques of the inverse moments problem, J. Math. Comput. Sci., 9 (2019), 239-253 Copyright © 2019 Maria B. Pintarelli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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