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October 8, 2025Open Access

Compensation effects for anisotropic energies of two-dimensional unit vector fields

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Authors

LBLia BronsardUniversity of TorontoDGDmitry GolovatyUniversity of AkronXLXavier LamyUniversité Toulouse III - Paul Sabatier

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Implication

This analysis reveals how anisotropic energy impacts compactness in unit vector fields, suggesting new insights into variational limits.

Key Points

  • Any bounded energy sequence achieves compactness in W^{s,3}_{ ext{loc}} for s<1/2, showing effective control despite energy loss.
  • Derivatives of order 1/2 remain controlled even as ε approaches 0, indicating optimal differentiability thresholds.
  • Establishes compactness for boundary traces in L^1(∂Ω), highlighting the importance of boundary behavior in energy analysis.
  • Characterizes the Γ-limit in simplified scenarios, including maps of a single variable and thin-film models.

Cite This Study

Bronsard et al. (2025) studied this question.

synapsesocial.com/papers/68e6679587ecc93a24d1759bhttps://doi.org/10.48550/arxiv.2507.17345
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