Hypoelliptic differential operators

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...

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...

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

Partial differential equations. -- Gaussian estimates for hypoelliptic operators via optimal control

Partial differential equations. — Gaussian estimates for hypoelliptic operators via optimal control, by UGO BOSCAIN and SERGIO POLIDORO, communicated on 11 May 2007. ABSTRACT. — We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitab...