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  1. ; (, Archive for Rational Mechanics and Analysis)
    We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equa- tion in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy and entropy densities are bounded above, and the mass density is bounded away from a vacuum, we obtain an estimate of the Lāˆž norm of the solution de- pending on the macroscopic bounds on these hydrodynamic quantities only. This is a regularization effect in the sense that the initial data is not required to be bounded. We present a proof based on variational ideas, which is fundamentally different to the proof that was previously known for the equation in periodic spatial domains 
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  2. ; (, Kinetic and Related Models)
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  3. (, Ars inveniendi analytica)
    We obtain local Holder continuity estimates up to the boundary for a kinetic Fokker-Planck equation with rough coefficients, with the prescribed influx boundary condition. Our result extends some recent developments that incorporate De Giorgi methods to kinetic Fokker-Planck equations. We also obtain higher order asymptotic estimates near the incoming part of the boundary. In particular, when the equation has a zero boundary conditions and no source term, we prove that the solution vanishes at infinite order on the incoming part of the boundary. 
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    Accepted Manuscript Full Text Available
  4. ; (, Journal of the American Mathematical Society)
    We derive C āˆž C^\infty a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to pointwise bounds on their mass, energy and entropy densities. We also establish decay estimates for large velocities, for all derivatives of the solution. 
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  5. (, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)
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  6. ; (, Mathematics in Engineering)
    The purpose of this paper is to show how the combination of the well-known results for convergence to equilibrium and conditional regularity, in addition to a short-time existence result, lead to a quick proof of the existence of global smooth solutions for the non cutoff Boltzmann equation when the initial data is close to equilibrium. We include a short-time existence result for polynomially-weighted $$ L^\infty $$ initial data. From this, we deduce that if the initial data is sufficiently close to a Maxwellian in this norm, then a smooth solution exists globally in time. 
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