A Fokker-Planck type approximation of parabolic PDEs with oblique boundary data
Damon Alexander, Inwon Kim · Transactions of the American Mathematical Society · 2015
We consider solutions of quasi-linear parabolic PDEs with zero oblique boundary data in a bounded domain. Our main result states that the solutions can be approximated by solutions of a Fokker-Planck type PDE in the whole space with a penalizing drift term which also converges to zero outside the original domain. The convergence is locally uniform, and optimal error estimates are obtained.