Regularity of Milne Problem with Geometric Correction in 3D

Yan Guo; Lei Wu

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arXiv · 1610.00172

Regularity of Milne Problem with Geometric Correction in 3D

Yan Guo·Lei Wu

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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.

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Yan Guo, Lei Wu. 2016-10-01. Regularity of Milne Problem with Geometric Correction in 3D. https://arxiv.org/abs/1610.00172

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