Reconstructing double-well potentials from transition layers in long-range phase coexistence models
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913015183441920 |
|---|---|
| author | Dipierro, Serena De Pas, Francesco Valdinoci, Enrico |
| author_facet | Dipierro, Serena De Pas, Francesco Valdinoci, Enrico |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06717 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reconstructing double-well potentials from transition layers in long-range phase coexistence models Dipierro, Serena De Pas, Francesco Valdinoci, Enrico Analysis of PDEs 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. |
| title | Reconstructing double-well potentials from transition layers in long-range phase coexistence models |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.06717 |