Global Irregularity for Mildly Degenerate Elliptic Operators

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

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.

Degenerate anisotropic elliptic problems and magnetized plasma simulations

This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem. The numerical method is designed for arbitrary space-dependent anisotropy directions and does not require any specially adapted coordinate system. It is also designed to be equally accurate in the strongly and the mildly anisotropic cases. The method is applied to the Euler-Lorentz system, in the ...

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...

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 ≤ ∫