Regularity of Milne Problem with Geometric Correction in 3D

Abstract

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish $W^{1,\infty}$ regularity for its solutions. Combined with a uniform $L^6$ estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.

52 pages. arXiv admin note: substantial text overlap with arXiv:1605.02362