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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

Lei Wu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA

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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