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Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. (English) Zbl 0934.45010

A particular type of the Boltzmann equation from the kinetic theory of gases is considered. The Boltzmann collision operator contains a kernel which is usually supposed to be locally integrable. Looking for smoothness estimates and according to physical point of view, the author considers it to be bounded from below by a singular (otherwise smooth) function in the origin \(O(1+\nu\) is the singularity order). If the entropy dissipation functional is finite; there the solution \(f\) satisfies \(\sqrt f\in H^{\nu/2}_{\text{loc}}\).

MSC:

45K05 Integro-partial differential equations
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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