On approximation of the Dirichlet problem for divergence form operators by Robin problems
Andrzej Rozkosz, Leszek Słomiński · Archiv der Mathematik · 2023
Abstract We show that, under natural assumptions, solutions of Dirichlet problems for uniformly elliptic divergence form operators can be approximated pointwise by solutions of some versions of Robin problems. The proof is based on the stochastic representation of solutions and properties of reflected diffusions corresponding to divergence form operators.