Kinetic equations are a class of possibly degenerate second-order partial differential evolution equations that model the diffusion of particle systems in phase space. Among the most classic examples that can be considered are the Kolmogorov-Fokker-Planck equation, the Boltzmann equation, and the Landau equation, which have various applications in physics and economics. By combining a priori estimates, potential theory, and variational methods, we study the well-posedness of boundary value problems (of the Cauchy and Dirichlet type) and the regularity (internal and up to the boundary) of weak solutions.
