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

Pablo  Ochoa

doi:10.3934/cpaa.2015.14.1841

Article Contents

2015, Volume 14, Issue 5: 1841-1863. Doi: 10.3934/cpaa.2015.14.1841

This issue Previous Article On the initial value problem of fractional stochastic evolution equations in Hilbert spaces Next Article Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces

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

Pablo Ochoa^1,

1.
Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo., Padre Contreras 1300, Parque Gral. San Martin. M5502JMA Mendoza

Received: August 31, 2014

Revised: February 28, 2015

Published: August 2015

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Abstract

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.

Keywords:

Partial differential equations on the Heisenberg group,
finite difference methods,
viscosity solutions,
Heisenberg group,
approximation schemes.

Mathematics Subject Classification: Primary: 35R03; Secondary: 65N06.

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References

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