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BIRS Workshop Lecture Videos

Weak Harnack inequality for the Boltzmann equation without cut-off Imbert, Cyril


In this talk, I will present the recent results obtained in collaboration with L. Silvestre (Chicago) about Hölder continuity of solutions of the Boltzmann equation without cut-off under the condition that mass, energy and density are locally bounded and that mass is bounded away from zero (non-vacuum condition). Such a regularity result is a consequence of a weak Harnack inequality for a general kinetic integro-differential equation for kernels satisfying sufficiently mild conditions to be applicable to the Boltzmann equation. Such a weak Harnack inequality is obtained by applying elliptic regularity techniques of De Giorgi type.

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