On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group

Abstract

In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's "principle of not feeling the boundary". This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.

14 pages

Cited by in corpus (2)

• On Green functions for Dirichlet sub-Laplacians on H-type groups
• Layer potentials, Green's formulae, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups