Regularity of Milne Problem with Geometric Correction in 3D

Yan Guo; Lei Wu

Regularity of Milne Problem with Geometric Correction in 3D

Analysis of PDEs 2016-10-04 v1

Authors: Yan Guo , Lei Wu

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.

Keywords

regularity theory convex geometry

Cite

@article{arxiv.1610.00172,
  title  = {Regularity of Milne Problem with Geometric Correction in 3D},
  author = {Yan Guo and Lei Wu},
  journal= {arXiv preprint arXiv:1610.00172},
  year   = {2016}
}

Comments

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

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