Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 114, pp. 111.
pharmonious functions with drift on graphs via games
Alexander P. Sviridov
Abstract:
In a connected finite graph
with set of vertices
,
choose a nonempty subset, not equal to
the whole set,
,
and call it the boundary
.
Given a realvalued function
, our objective
is to find a function
, such that
on
, and
for all
,
Here
are nonnegative constants such that
, the set
is the collection of vertices connected to
by an edge, and
denotes its cardinality.
We prove the existence and uniqueness of a solution of the above
Dirichlet problem and study the qualitative properties of the solution.
Submitted October 26, 2010. Published September 6, 2011.
Math Subject Classifications: 35Q91, 35B51, 34A12, 31C20.
Key Words: Dirichlet problem; comparison principle; meanvalue property;
stochastic games; unique continuation.
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Alexander P. Sviridov
Department of Mathematics,
University of Pittsburgh
Pittsburgh, PA 15260, USA
email:aps14@pitt.edu

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