Γ-convergence of higher-order phase transition models
We investigate the asymptotic behavior as ɛ→0 of singularly perturbed phase transition models of order n≥2, given by Gɛλ,n[u]≔∫I1ɛW(u)−λɛ2n−3(u(n−1))2+ɛ2n−1(u(n))2dx,u∈Wn,2(I),where λ>0 is fixed, I⊂R is an open bounded interval, and W∈C0(R) is a suitable double-well potential. We find that there...
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| Auteurs principaux: | , , |
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| Format: | Article (Journal) |
| Langue: | anglais |
| Publié: |
February 2026
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| In: |
Nonlinear analysis. Theory, methods & applications
Year: 2026, Volume: 263, Pages: 1-17 |
| ISSN: | 1873-5215 |
| DOI: | 10.1016/j.na.2025.113971 |
| Accès en ligne: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.na.2025.113971 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0362546X25002238 
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| Notes sur l'auteur: | Denis Brazke, Gianna Götzmann, Hans Knüpfer |
| Résumé: | We investigate the asymptotic behavior as ɛ→0 of singularly perturbed phase transition models of order n≥2, given by Gɛλ,n[u]≔∫I1ɛW(u)−λɛ2n−3(u(n−1))2+ɛ2n−1(u(n))2dx,u∈Wn,2(I),where λ>0 is fixed, I⊂R is an open bounded interval, and W∈C0(R) is a suitable double-well potential. We find that there exists a positive critical parameter depending on W and n, such that the Γ-limit of Gɛλ,n with respect to the L1-topology is given by a sharp interface functional in the subcritical regime. The cornerstone for the corresponding compactness property is a novel nonlinear interpolation inequality involving higher-order derivatives, which is based on Gagliardo-Nirenberg type inequalities. |
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| Description: | Gesehen am 29.05.2026 |
| Description matérielle: | Online Resource |
| ISSN: | 1873-5215 |
| DOI: | 10.1016/j.na.2025.113971 |