On Neumann Type Problems for nonlocal Equations set in a half Space

Details On Neumann Type Problems for nonlocal Equations set in a half Space On Neumann Type Problems for nonlocal Equations set in a half Space

2011-12-02

arxiv.org/abs/1112.0476v1

Mathematics

Analysis of PDEs

Scientific paper

We study Neumann type boundary value problems for nonlocal equations related to L\'evy processes. Since these equations are nonlocal, Neumann type problems can be obtained in many ways, depending on the kind of reflection we impose on the outside jumps. To focus on the new phenomenas and ideas, we consider different models of reflection and rather general non-symmetric L\'evy measures, but only simple linear equations in half-space domains. We derive the Neumann/reflection problems through a truncation procedure on the L\'evy measure, and then we develop a viscosity solution theory which includes comparison, existence, and some regularity results. For problems involving fractional Laplacian type operators like e.g.$(-\Delta)^{\alpha/2}$, we prove that solutions of all our nonlocal Neumann problems converge as alpha goes to 2 to the solution of a classical Neumann problem. The reflection models we consider include cases where the underlying L\'evy processes are reflected, projected, and/or censored upon exiting the domain.

Affiliated with

Also associated with

No associations

Rating

On Neumann Type Problems for nonlocal Equations set in a half Space 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 On Neumann Type Problems for nonlocal Equations set in a half Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Neumann Type Problems for nonlocal Equations set in a half Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-140427