Elisabetta Barletta and Sorin Dragomir: Sublaplacians on CR manifolds, p.3-32

Abstract:

We study the sublaplacian $\Delta_b$ on a strictly pseudoconvex CR manifold endowed with a contact form. $\Delta_b$ is approximated by a continuous family of second order elliptic operators $\{ \Delta_\epsilon \}_{\epsilon > 0}$. If $\{ \Delta_\epsilon \}_{\epsilon > 0}$ is uniformly $K$-positive definite (in the sense of W.V. Petryshyn) then we produce generalized solutions to $\Delta_b u = f$.

Key Words: CR manifold, Webster metric, sub-Riemannian gradient, sublaplacian.

2000 Mathematics Subject Classification: Primary: 32V20,
Secondary: 35H20, 53C17.

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