Degenerate elliptic operators: capacity, flux and separation

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

On Local Properties of Some Classes of Infinitely Degenerate Elliptic Differential Operators

We give necessary and sufficient conditions for local solvability and hypoellipticity of some classes of infinitely degenerate elliptic differential operators.

Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫

Control and Cybernetics Generation of Analytic Semi-groups in L 2 for a Class of Second Order Degenerate Elliptic Operators *

Abstract: We study the generation of analytic semigroups in the L topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimensions, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type es...