Calculus of Variations and Geometric Measure Theory

F. P. Maiale - G. Tortone - B. Velichkov

The boundary Harnack principle on optimal domains

created by velichkov on 10 May 2022



Inserted: 10 may 2022
Last Updated: 10 may 2022

Year: 2021

ArXiv: 2112.01217 PDF


We give a short 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.