On the comparison of Boltzmann and Landau collision integrals

The estimate for the difference of the Landau collision integral and the Boltzmann collision integral with delta-kernel is obtained. The estimate holds in a class of smooth and rapidly decreasing at infinity distribution functions. It is proved in the general case of multicomponent gas mixture. Results can be used for theoretical and numerical problems related to the nonlinear Landau–Fokker–Planck kinetic equation.