Approximation schemes for non-linear second order equations on the Heisenberg group

PABLO OCHOA

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

AMER INST MATHEMATICAL SCIENCES

Año: 2015 vol. 14 p. 1841 - 1863

1534-0392

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.