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Main Author: Candau-Tilh, Jules
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2406.16379
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author Candau-Tilh, Jules
author_facet Candau-Tilh, Jules
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_16379
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A concentration-compactness principle for perturbed isoperimetric problems with general assumptions
Candau-Tilh, Jules
Analysis of PDEs
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.
title A concentration-compactness principle for perturbed isoperimetric problems with general assumptions
topic Analysis of PDEs
url https://arxiv.org/abs/2406.16379