The Dirichlet problem for the Kohn Laplacian on the Heisenberg group,II |
| |
Authors: | David S Jerison |
| |
Institution: | Department of Mathematics, University of Chicago, Chicago, Illinois 60637 USA |
| |
Abstract: | Let L = ∑j = 1mXj2 be sum of squares of vector fields in n satisfying a Hörmander condition of order 2: span{Xj, Xi, Xj]} is the full tangent space at each point. A point x??D of a smooth domain D is characteristic if X1,…, Xm are all tangent to ?D at x. We prove sharp estimates in non-isotropic Lipschitz classes for the Dirichlet problem near (generic) isolated characteristic points in two special cases: (a) The Grushin operator in 2. (b) The real part of the Kohn Laplacian on the Heisenberg group in 2n + 1. In contrast to non-characteristic points, C∞ regularity may fail at a characteristic point. The precise order of regularity depends on the shape of ?D at x. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|