The Poisson kernel for certain degenerate elliptic operators

Global Irregularity for Mildly Degenerate Elliptic Operators

Examples are given of degenerate elliptic operators on smooth, compact manifolds that are not globally regular in C∞. These operators degenerate only in a rather mild fashion. Certain weak regularity results are proved, and an interpretation of global irregularity in terms of the associated heat semigroup is given.

Finite Difference Methods for the Computation of the "Poisson Kernel" of Elliptic Operators

Degenerate Hypoelliptic Operators and the Gaussian Kernel

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

The Harnack inequality for a class of degenerate elliptic operators

We prove a Harnack inequality for distributional solutions to a type of degenerate elliptic PDEs in N dimensions. The differential operators in question are related to the Kolmogorov operator, made up of the Laplacian in the last N−1 variables, a first-order term corresponding to a shear flow in the direction of the first variable, and a bounded measurable potential term. The first-order coeffi...