APPROXIMATION SCHEMES FOR NON-LINEAR SECOND ORDER EQUATIONS ON THE HEISENBERG GROUP

摘要

In this work, we propose and analyse approximation schemes for fully non-linear second order partial differential equations defined on the Heisenberg group. We prove that a consistent, stable and monotone scheme converges to a viscosity solution of a second order PDE on the Heisenberg group provided that comparison principles exists for the limiting equation. We also provide examples where this technique is applied.