The Harnack inequality for a class of degenerate elliptic operators

And Pointwise Estimates for a Class of Degenerate Elliptic Equations

In this paper we prove a Sobolev-Poincaré inequality for a class of function spaces associated with some degenerate elliptic equations. These estimates provide us with the basic tool to prove an invariant Harnack inequality for weak positive solutions. In addition, Holder regularity of the weak solutions follows in a standard way. 1 Let Sf = YJl ,=i 9j(ajjdj) be a second-order degenerate ellipt...

Harnack inequalities and Bôcher-type theorems for conformally invariant fully nonlinear degenerate elliptic equations

We give a generalization of a theorem of Bôcher for the Laplace equation to a class of conformally invariant fully nonlinear degenerate elliptic equations. We also prove a Harnack inequality for locally Lipschitz viscosity solutions and a classification of continuous radially symmetric viscosity solutions.

On the Harnack Inequality for a Class of Hypoelliptic Evolution Equations

We give a direct proof of the Harnack inequality for a class of degenerate evolution operators which contains the linearized prototypes of the Kolmogorov and Fokker-Planck operators. We also improve the known results in that we find explicitly the optimal constant of the inequality.

Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form

We prove some Schauder type estimates and an invariant Harnack inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators