The weak Harnack inequality for the Boltzmann equation without cut-off
By C. Imbert, Luis Silvestre. Journal of the European Mathematical Society (Print), 2016
118 citations recorded by the source corpus.
In this paper, we obtain the weak Harnack inequality and Holder estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can be written in this form and satisfies our assumptions provided that the mass density is bounded away from vacuum and mass, energy and entropy densities are bounded above. As a consequence, we derive a local Holder estimate and a quantitative lower bound for solutions of the (inhomogeneous) Boltzmann equation without cut-off.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4789bf044e637946573458007d335cf4234d90c9
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In Applied Mathematics
- Luis Silvestre
- C. Imbert
- Dallas Albritton
- Matthew Novack
- Rajendra Beekie
- Russell W. Schwab
- Juan Luis V'azquez
- Enrico Valdinoci
In Mathematical Physics
- C. Imbert
- Luis Silvestre
- Dallas Albritton
- Matthew Novack
- Rajendra Beekie
- Juan Luis V'azquez
- Pablo Raúl Stinga
- Enrico Valdinoci
Citations in the corpus
- The Schauder estimate for kinetic integral equations (2018, methodology): “We use the same notation as in [10]: Qr denotes the kinetic cylinder Qr := (−r, 0]×Br1+2s ×Br.”
- Enhanced dissipation and Hörmander's hypoellipticity (2021, methodology): “In [41], Silvestre derived a priori Hölder estimates for the Boltzmann equation, and follow-up work of Silvestre and Imbert [33] obtained weak Harnack and Hölder estimates for a large class of integro-differential equations, including the Boltzmann equation without cutoff.”