  We consider a Laplacian on the one-sided full shift space over a finite
symbol set, which is constructed as a renormalized limit of finite difference
operators. We propose a weak definition of this Laplacian, analogous to the one
in calculus, by choosing test functions as those which have finite energy and
vanish on various boundary sets. In the abstract setting of the shift space,
the boundary sets are chosen to be the sets on which the finite difference
operators are defined. We then define the Neumann derivative of functions on
these boundary sets and establish a relation between three important concepts
in analysis so far, namely, the Laplacian, the bilinear energy form and the
Neumann derivative of a function. As a result, we obtain the Gauss-Green's
formula analogous to the one in classical case. We conclude this paper by
providing a sufficient condition for the Neumann boundary value problem on the
shift space.
