$W^{1, p}$ estimate for the stationary transport equation


Astro-Math Bldg. 202

Day and Time: 

2019-06-03 (Monday) 14:00 - 15:00


We consider a boundary value problem of the stationary transport equation in a two dimensional bounded convex domain with the incoming boundary condition. In this talk, we give a $W^{1, p}$ estimate of the solution for $1 \leq p < p_m$, where $p_m$ is a real number depending only on the shape of the domain. Moreover, we show two examples which imply that this estimate is optimal in some cases.