In the present paper we consider the Dirichlet problem for the n- dimensional Helmholtz equation. In particular we deal with the problem of rep- resentability of the solutions by means of simple layer potentials. The main result concerns the solvability of a boundary integral equation of the first kind. Such a result is here obtained by using the theories of differential forms and reducible operators.
On the Simple Layer Potential Ansatz for the n-Dimensional Helmholtz Equation
Cialdea, Alberto;Leonessa, Vita;Malaspina, Angelica
2020-01-01
Abstract
In the present paper we consider the Dirichlet problem for the n- dimensional Helmholtz equation. In particular we deal with the problem of rep- resentability of the solutions by means of simple layer potentials. The main result concerns the solvability of a boundary integral equation of the first kind. Such a result is here obtained by using the theories of differential forms and reducible operators.File in questo prodotto:
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