Published Paper

Inserted: 3 aug 2026
Last Updated: 3 aug 2026

Journal: In: New Frontiers in Homogenization and Fractional Calculus (Duran i Lamiel, J., Maione, A. eds). Trends in Mathematics. Birkhäuser, Cham.
Pages: 1--20
Year: 2026
Doi: 10.1007/978-3-032-20098-3_1

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.