Publication 16-CNA-022

Regularity of Milne Problem with Geometric Correction in 3D

Yan Guo
Division of Applied Mathematics
Brown University
Providence, RI 02912, USA
guoy@dam.brown.edu

Lei Wu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
lwu2@andrew.cmu.edu

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.

Get the paper in its entirety as  16-CNA-022.pdf

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