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
modified on 07 Oct 2024

[BibTeX]

Published Paper

Inserted: 10 may 2022
Last Updated: 7 oct 2024

Journal: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Year: 2024
Doi: https://doi.org/10.2422/2036-2145.202112_003

ArXiv: 2112.01217 PDF

Abstract:

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.


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