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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16379 |
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| _version_ | 1866917703277608960 |
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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 |