2/4/2005

Jih-Hsin Cheng
Academica Sinica, Taipei

Existence and uniqueness for p-minimizers in the Heisenberg group

We consider the p-minimal graph equation in the Heisenberg group. This is a degenerate elliptic and hyperbolic PDE in dimension 2 and a subelliptic equation in the nonsingular domain for higher dimensions. Moreover, it is the Euler-Lagrange equation associated to a degenerate energy functional. In this talk, we will prove the existence of a Lipschitz continuous minimizer for such an energy functional with a given boundary value. We will also show the uniqueness of minimizers. Besides, we will give an example to show the impossibility of getting better regularity for a C^1 minimizer having a smooth boundary value in dimension 2.