On Green functions for Dirichlet sub-Laplacians on H-type groups

Abstract

We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group, in short). We also present solutions in an explicit form of the Dirichlet problem for the sub-Laplacian with non-zero boundary datum on half-space, quadrant-space, etc, as well as in a strip.

11 pages, to appear in JMAA

References in corpus (2)

• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and $p$-sub-Laplacian inequalities on stratified groups
• Local Hardy and Rellich inequalities for sums of squares of vector fields

Cited by in corpus (2)

• Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
• A Neumann type problem on an unbounded domain in the Heisenberg group