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A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation (2407.08785v1)
Published 11 Jul 2024 in math.AP
Abstract: In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on the half-space. As an application, we address the boundary behavior of the kinetic Fokker-Planck equations in the half-space. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set.