Proves optimal C^{3/2} (smooth data) and C^{1,1} (no sources) boundary Harnack estimates for kinetic Fokker-Planck equations near grazing sets.
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Extends De Giorgi-Nash-Moser theory to nonlocal hypoelliptic kinetic equations, proving local L²-L^∞ estimates and strong Harnack inequalities for weak solutions under a p-summable nonlocal velocity tail condition along drift variables.
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Boundary Harnack estimates of optimal order for kinetic Fokker-Planck equations
Proves optimal C^{3/2} (smooth data) and C^{1,1} (no sources) boundary Harnack estimates for kinetic Fokker-Planck equations near grazing sets.
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De Giorgi-Nash-Moser theory for kinetic equations with nonlocal diffusions
Extends De Giorgi-Nash-Moser theory to nonlocal hypoelliptic kinetic equations, proving local L²-L^∞ estimates and strong Harnack inequalities for weak solutions under a p-summable nonlocal velocity tail condition along drift variables.