ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP

ABSTRACT

In this paper, we study infinite harmonic functions in the viscosity sense on the Heisenberg group. Existence of infinite harmonic functions in the viscosity sense is proved following the scheme of Bhatthacharya, DiBenedetto, and Manfredi [1] while uniqueness of infinite harmonic functions is proved using an extension of Jensen's proof [2]. Both the existence and uniqueness proofs utilize the concept of subelliptic jets. By establishing a natural relationship between Euclidean and subelliptic jets, the technology of viscosity solutions found in [3] can be used.

Keywords:

• Viscosity solutions
• Heisenberg group
• 1991 Mathematics Subject Classification
• Primary: 35J70
• Secondary: 22E25

Acknowledgments