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arXiv · 2604.10909

Long-range phase coexistence models with degenerate potentials

Francesco De Pas·Serena Dipierro·Enrico Valdinoci
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Abstract

This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus (\R^n \setminus \Omega)^2} \frac{|u(x)-u(y)|^2}{|x-y|^{n+2s}}\,dx\,dy \;+\; \int_\Omega W(u(x))\,dx. \] Here,~$W$ is a smooth and possibly \textit{degenerate} double well potential, with a polynomial control on its second derivatives near the wells. The emphasis is on qualitative properties of minimizers and critical points of the energy functional.

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Francesco De Pas, Serena Dipierro, Enrico Valdinoci. 2026-04-13. Long-range phase coexistence models with degenerate potentials. https://arxiv.org/abs/2604.10909

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