A partial regularity result for a class of stationary Yang-Mills fields in high dimension.
From MaRDI portal
Publication:1413723
DOI10.4171/RMI/343zbMath1127.35317OpenAlexW2047701972MaRDI QIDQ1413723
Publication date: 17 November 2003
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.rmi/1049123085
Gauge TheoryInterpolation inequalitiesMorrey SpacesNonlinear elliptic regularity theoryYang-Mills Fields
Nonlinear elliptic equations (35J60) PDEs in connection with quantum mechanics (35Q40) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)
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Cites Work
- Unnamed Item
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- A monotonicity formula for Yang-Mills fields
- Compactness of the moduli space of Yang-Mills connections in higher dimensions
- Connections with \(L^ p \)bounds on curvature
- Partial regularity for stationary harmonic maps into spheres
- A note on Riesz potentials
- Gauge theory and calibrated geometry. I
- Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
- A singularity removal theorem for Yang-Mills fields in higher dimensions
