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Tobias Kaiser

Definability results for the Poisson equation

We show that the solution of the Poisson equation with subanalytic data on a bounded subanalytic domain in the plane without isolated boundary points exists and we prove that the solution is definable in the o-minimal structure ℝ_{an; exp}, provided that the domain has smooth boundary. Moreover, we investigate whether the solution is again subanalytic. At the end, we study polygons as examples of domains with nonsmooth boundary.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 6, 10/2006
Pages: 627 - 644

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