The mixed problem for harmonic functions in polyhedra

Details The mixed problem for harmonic functions in polyhedra The mixed problem for harmonic functions in polyhedra

2008-03-06

arxiv.org/abs/0803.0957v1

Mathematics

Analysis of PDEs

Scientific paper

R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2) manifold boundaries that are not locally given as the graphs of functions. Examples are constructed to illustrate necessity and other implications of the geometric hypotheses.

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