A concentration-compactness principle for perturbed isoperimetric problems with general assumptions
Analysis of PDEs
2024-06-25 v1
Abstract
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article and under mild assumptions we establish existence and density estimates of generalized minimizers of perturbed isoperimetric problems. Our hypotheses encapsulate a wide class of functionals including the classical, anisotropic and fractional perimeter. The perturbation term may for instance take the form of a potential, a translation invariant kernel or a nonlocal term involving the Wasserstein distance.
Cite
@article{arxiv.2406.16379,
title = {A concentration-compactness principle for perturbed isoperimetric problems with general assumptions},
author = {Jules Candau-Tilh},
journal= {arXiv preprint arXiv:2406.16379},
year = {2024}
}