Tony Perkins
Published 2014-06-24Version 1
In classical potential theory, one can solve the Dirichlet problem on unbounded domains such as the upper half plane. These domains have two types of boundary points; the usual finite boundary points and another point at infinity. W. Woess has solved a discrete version of the Dirichlet problem on the ends of graphs analogous to having multiple points at infinity and no finite boundary. Whereas C. Kiselman has solved a similar version of the Dirichlet problem on graphs analogous to bounded domains. In this work, we combine the two ideas to solve a version of the Dirichlet problem on graphs with finitely many ends and boundary points of the Kiselman type.
$C^{1, 1}$ Solution of the Dirichlet Problem for Degenerate $k$-Hessian Equations
Applications of Fourier analysis in homogenization of Dirichlet problem III: Polygonal Domains
The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz Domains
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