Stable solutions of symmetric systems involving hypoelliptic operators

Spectral Properties of Hypoelliptic Operators

We study hypoelliptic operators with polynomially bounded coefficients that are of the form K = ∑m i=1 X i Xi + X0 + f , where the Xj denote first order differential operators, f is a function with at most polynomial growth, and X i denotes the formal adjoint of Xi in L. For any ε > 0 we show that an inequality of the form ‖u‖δ,δ ≤ C(‖u‖0,ε + ‖(K + iy)u‖0,0) holds for suitable δ and C which are...

Semilinear Hypoelliptic Differential Operators with Multiple Characteristics

In this paper we consider the regularity of solutions of semilinear differential equations principal parts of which consist of linear polynomial operators constructed from real vector fields. Based on the study of fine properties of the principal linear parts we then obtain the regularity of solutions of the nonlinear equations. Some results obtained in this article are also new in the frame of...

H∞-calculus for Hypoelliptic Pseudodifferential Operators

We establish the existence of a bounded H∞-calculus for a large class of hypoelliptic pseudodifferential operators on R and closed manifolds.

Degenerate Hypoelliptic Operators and the Gaussian Kernel

Existence of Solutions for Non-necessarily Cooperative Systems Involving Schrödinger Operators

We study the existence of a solution for a non-necessarily cooperative system of n equations involving Schrödinger operators defined on RN and we study also a limit case (the Fredholm Alternative (FA)). We derive results for semilinear systems. 2000 Mathematics Subject Classification. 35J10, 35J45.