Non-local singular perturbations of non-convex functionals -- recent results
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911372187533312 |
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| author | Braides, Andrea |
| author_facet | Braides, Andrea |
| contents | Singular perturbations have been used to select solutions of (non-convex) variational problems with a multiplicity of minimizers. The prototype of such an approach is the gradient theory of phase transitions by L. Modica, who specialized some earlier Gamma-convergence results by himself and S. Mortola contained in a seminal paper, validating the so-called minimal-interface criterion. I will give an overview of some recent results on perturbations with fractional and higher-order seminorms both in the framework of phase transitions and of free-discontinuity problems, relating these results with the Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova limit analysis for fractional Sobolev seminorms, and with the theory of Gamma-expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-local singular perturbations of non-convex functionals -- recent results Braides, Andrea Analysis of PDEs Mathematical Physics 49J45, 35B25, 82B26, 35R11 Singular perturbations have been used to select solutions of (non-convex) variational problems with a multiplicity of minimizers. The prototype of such an approach is the gradient theory of phase transitions by L. Modica, who specialized some earlier Gamma-convergence results by himself and S. Mortola contained in a seminal paper, validating the so-called minimal-interface criterion. I will give an overview of some recent results on perturbations with fractional and higher-order seminorms both in the framework of phase transitions and of free-discontinuity problems, relating these results with the Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova limit analysis for fractional Sobolev seminorms, and with the theory of Gamma-expansions. |
| title | Non-local singular perturbations of non-convex functionals -- recent results |
| topic | Analysis of PDEs Mathematical Physics 49J45, 35B25, 82B26, 35R11 |
| url | https://arxiv.org/abs/2601.08573 |