Boundary value problems on product domains

Details Boundary value problems on product domains Boundary value problems on product domains

2005-02-15

arxiv.org/abs/math/0502309v3

Mathematics

Analysis of PDEs

12 pages

Scientific paper

We consider the inhomogeneous Dirichlet problem on product domains. The main
result is the asymptotic expansion of the solution in terms of increasing
smoothness up to the boundary. In particular, we show the exact nature of the
singularities of the solution at singularities of the boundary by constructing
singular functions which make up an asymptotic expansion of the solution.

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