Invariant Measures Associated to Degenerate Elliptic Operators

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

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.

On a class of degenerate elliptic operators arising from Fleming-Viot processes

We are dealing with the solvability of an elliptic problem related to a class of degenerate second order operators which arise from the theory of Fleming-Viot processes in population genetics. In the one dimensional case the problem is solved in the space of continuous functions. In higher dimension we study the problem in L2 spaces with respect to an explicit measure which, under suitable assu...

Sharp upper bounds for the density of some invariant measures

We prove sharp upper bounds for invariant measures of Markov processes in R associated with second-order elliptic differential operators with unbounded coefficients. Mathematics subject classification (2000): 35J70, 35B65, 47D07.