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arXiv · 2601.08573

Non-local singular perturbations of non-convex functionals -- recent results

Andrea Braides
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Abstract

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.

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Andrea Braides. 2026-01-13. Non-local singular perturbations of non-convex functionals -- recent results. https://arxiv.org/abs/2601.08573

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