Interior Regularity for Two-Dimensional Stationary Q-Valued Maps

Interior Regularity for Two-Dimensional Stationary Q-Valued Maps

We prove that 2-dimensional Q -valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for...

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Veröffentlicht in:Archive for rational mechanics and analysis 2024-08, Vol.248 (4), p.67, Article 67
Hauptverfasser: Hirsch, Jonas, Spolaor, Luca
Format: Artikel
Sprache:eng
Schlagworte:
Classical Mechanics
Complex Systems
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Energy
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung:We prove that 2-dimensional Q -valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-024-02011-w