On approximation of the Dirichlet problem for divergence form operator by Robin problems
Analysis of PDEs
2023-10-05 v2 Probability
Abstract
We show, that under natural assumptions, solutions of Dirichlet problems for uniformly elliptic divergence form operator can be approximated pointwise by solutions of some versions of Robin problems. The proof is based on stochastic representation of solutions and properties of reflected diffusions corresponding to divergence form operators.
Cite
@article{arxiv.2205.08396,
title = {On approximation of the Dirichlet problem for divergence form operator by Robin problems},
author = {Andrzej Rozkosz and Leszek Slominski},
journal= {arXiv preprint arXiv:2205.08396},
year = {2023}
}