Solutions for nonhomogeneous Kohn–Spencer Laplacian on Heisenberg group

Abstract

In this paper, we study the existence of at least one bounded weak solution for Kohn–Spencer Laplacian with a weight depending on the solution and convection term of the form − d i v H n ( ν ( ξ , u ) | D H n u | H n p − 2 D H n u ) = f ( ξ , u , D H n u ) in a bounded domain Ω ⊂ H n . We show the set of solutions is uniformly bounded by a special Moser's iteration.