| Abstract: |
| We present a study on the boundary behavior of a kinetic Fokker-Planck equation in the half-space with absorbing boundary condition. This equation can be seen as a base model for the study of Boltzmann equations: although the kinetic equation that we are taking into account is linear and present a local diffusion, it shares with the Boltzmann equation an analogue hypoelliptic structure. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set. The technique is based on a new kinetic Nash-type inequality. This talk is based on a joint work with Christopher Henderson (University of Arizona) and Weinan Wang (University of Oklahoma). |
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