Dynamics of many particle system can be described by PDE of probability density function. The Boltzmann equation in kinetic theory is one of the most famous equation which describes rarefied gas dynamics. One of main property of the Boltzmann is decaying to equilibrium as time goes to infinity. This equation and its asymptotics has been studied for several decades ago, but boundary problem of the Boltzmann equation has been widely open because of singular behavior of boundary Boltzmann problem. We introduce new framework to study pointwise behavior of the equation in general boundary problems.
