The Fokker-Planck equation with absorbing boundary conditions in bounded domains

Abstract

In this paper, we study the initial-boundary value problem of the Fokker-Planck equation with absorbing boundary conditions in multidimensional bounded domains. First, we establish a well-posedness theory by constructing a solution for the regularized equation and passing to the limit by uniform L-1 and L-infinity estimates. Second, for a general multidimensional domain with a smooth boundary, we show that the solution is smooth far from the singular set and locally Holder continuous up to the singular set.