Energy decay for the neutrino equation in the exterior of a torus

Abstract

Local energy decay is established for the solutions of the neutrino equation in the exterior G of a torus for a class of boundary conditions, described as follows: To each energy conserving boundary condition at a point x on ∂G there corresponds a vector in the tangent plane to ∂G at x. The result has been proved when the torus and boundary conditions are axially symmetric and when the paths generated by this vector field are closed. What is novel about this problem is the fact that the boundary conditions are nowhere coercive.