Date
2006
Dewey
Probabilités et Mathématiques appliquées
Sujet
coercivity estimates ; linearized Boltzmann operator ; linearized Landau operator ; quantitative ; soft potentials ; hard potentials ; spectral gap
Journal issue
Communications in Partial Differential Equations
Volume
31
Number
9
Publication date
09-2006
Article pages
1321 - 1348
Publisher
Taylor & Francis
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators, for a general class of interactions including any inverse-power law interactions, and hard spheres. The functional spaces of these coercivity estimates depend on the collision kernel of these operators. They cover the spectral gap estimates for the linearized Boltzmann operator with Maxwell molecules, improve these estimates for hard potentials, and are the first explicit coercivity estimates for soft potentials (including in particular the case of Coulombian interactions). We also prove a regularity property for the linearized Boltzmann operator with non locally integrable collision kernels, and we deduce from it a new proof of the compactness of its resolvent for hard potentials without angular cutoff.