The boundary Harnack principle on optimal domains
Analysis of PDEs
2024-02-13 v3
Abstract
We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.
Keywords
Cite
@article{arxiv.2112.01217,
title = {The boundary Harnack principle on optimal domains},
author = {Francesco Paolo Maiale and Giorgio Tortone and Bozhidar Velichkov},
journal= {arXiv preprint arXiv:2112.01217},
year = {2024}
}