LpLp-solutions of Fokker–Planck equations

•Existence and uniqueness of weak LpLp-solutions for Fokker–Planck equations are obtained.•Applied the transport theory, the generalized Itô formula and the renormalization technique.•The method is a little different from the classical partial differential equation tools.

We obtain the existence and uniqueness of LpLp-solutions (1≤p≤∞1≤p≤∞) for Fokker–Planck equations with irregular and degenerate coefficients. Moreover, as an application, we also derive the existence and uniqueness of L1L1-solutions for the Fokker–Planck–Boltzmann equation.