Regularity of Milne Problem with Geometric Correction in 3D
classification
🧮 math.AP
keywords
regularitycorrectiondiffusivegeometricmilneproblemargumentsbootstrapping
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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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