A monotonicity formula for a classical free boundary problem
Analysis of PDEs
2025-04-03 v1
Abstract
We construct a monotonicity formula for the free boundary problem of the form , where is a Radon measure. It implies that the blow up limits of solutions are homogenous functions of degree one. The first formula is new even for classical Laplace operator. Our method of proof uses a careful application of the strong maximum principle.
Cite
@article{arxiv.2504.01178,
title = {A monotonicity formula for a classical free boundary problem},
author = {Aram Karakhanyan},
journal= {arXiv preprint arXiv:2504.01178},
year = {2025}
}