The mixed problem for harmonic functions in polyhedra
Analysis of PDEs
2008-03-07 v1
Abstract
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.
Cite
@article{arxiv.0803.0957,
title = {The mixed problem for harmonic functions in polyhedra},
author = {Moises Venouziou and Gregory C. Verchota},
journal= {arXiv preprint arXiv:0803.0957},
year = {2008}
}