The Square of the Dirichlet-to-Neumann map equals minus Laplacian

Details The Square of the Dirichlet-to-Neumann map equals minus Laplacian The Square of the Dirichlet-to-Neumann map equals minus Laplacian

2008-06-03

arxiv.org/abs/0806.0653v1

Mathematics

General Mathematics

6 pages, 2 figures

Scientific paper

The Dirichlet-to-Neumann maps connect boundary values of harmonic functions. It is an amazing fact that the square of the non-local Dirichlet-to-Neumann map for the uniform conductivity 1 on the unit disc equals minus the local(!) Laplace operator on the boundary circle. To establish a new connection between discrete and continuous Dirichlet-to-Neumann maps and for the approximations I construct a finite and an infinite graphs which Dirichlet-to-Neumann map have the same property: \Lambda^2(1) = - d^2/d \theta^2. The construction gives a new continued fraction identity. It is interesting to consider the geometric and probabilistic (trajectories of the random walk) consequences of this localizing identity unifying discrete and continuous equations for potentials.

Affiliated with

Also associated with

No associations

Rating

The Square of the Dirichlet-to-Neumann map equals minus Laplacian does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Square of the Dirichlet-to-Neumann map equals minus Laplacian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Square of the Dirichlet-to-Neumann map equals minus Laplacian will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-153853