Reconstructing double-well potentials from transition layers in long-range phase coexistence models
Analysis of PDEs
2026-04-09 v1
Abstract
In models of phase coexistence, the precise form of the double-well potential is of central importance, yet it cannot be derived from first principles. In this paper, we investigate an inverse problem: starting from a prescribed transition layer with power-type decay at infinity, we reconstruct the structural properties of the associated double-well potential. We focus on the case of long-range interactions, where the dependence of the potential on the layer and its derivatives is particularly delicate. Our analysis establishes a correspondence between the decay rate of the transition layer and the regularity of the potential, revealing the existence of specific patterns and the possible emergence of degeneracies.
Keywords
Cite
@article{arxiv.2604.06717,
title = {Reconstructing double-well potentials from transition layers in long-range phase coexistence models},
author = {Serena Dipierro and Francesco De Pas and Enrico Valdinoci},
journal= {arXiv preprint arXiv:2604.06717},
year = {2026}
}