We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators . If is a positive weight such that , then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.
The aim of this paper is to show how, in order to prove regularity theorems, Hölder estimates, i.e. estimates involving products of powers of different semi-norms, can be used as well as standard estimates, and may in some instances be casier to prove.
We establish homogenization results for both linear and semilinear partial differential equations of parabolic type, when the linear second order PDE operator satisfies a hypoellipticity asumption, rather than the usual ellipticity condition. Our method of proof is essentially probabilistic.
This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations,...