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This is a Quantitative Study study.

September 30, 2025Open Access

Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials

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Authors

FPFrancesco De PasThe University of Western Australia SDSerena DipierroThe University of Western Australia MPMirco PiccininiUniversity of Pisa

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Implication

Analysis demonstrates existence and uniqueness of minimizers for non-local energy functionals, indicating potential application in mathematical physics.

Key Points

Existence and uniqueness of minimizers established for a class of energy functionals, shedding light on their asymptotic behavior.
The analysis reveals the interplay between degeneracy in potential and the behavior of minimizers under non-local conditions.
Utilizing a framework built on fractional Laplacian facilitates deeper insights into the energy landscape of these functionals.
Implications extend to mathematical models representing phase transitions and pattern formation phenomena.

Cite This Study

Pas et al. (2025) studied this question.

synapsesocial.com/papers/68dc12c58a7d58c25ebb0a61 https://doi.org/10.48550/arxiv.2505.20054

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Implication

Analysis demonstrates existence and uniqueness of minimizers for non-local energy functionals, indicating potential application in mathematical physics.

Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials

Discussion

Member takes

Implication

Key Points

Cite This Study

Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials

Discussion

Member takes

Implication

Key Points

Cite This Study

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