# zbMATH — the first resource for mathematics

The isolated point singularity problem for the coupled Yang-Mills equations in higher dimensions. (English) Zbl 0544.35082
An elementary proof of the removable point singularity theorem is given in dimensions $$n\geq 5$$. A gradient estimate on curvature is obtained in the neighborhood of the possible singularity by making an appropriate choice of test function. Subelliptic theory and the Morrey-Moser iteration are used to show that the curvature is bounded. Standard elliptic theory then implies that the solution of the field equations is gauge equivalent to a smooth configuration.

##### MSC:
 35Q99 Partial differential equations of mathematical physics and other areas of application 35A20 Analyticity in context of PDEs 81T08 Constructive quantum field theory
Full Text:
##### References:
 [1] Brezis, H., Veron, L.: Removable singularities for some non-linear elliptic equations. Archive for Ration. Mech. Anal.75, 1-6 (1980) [2] Gidas, B., Spruck, J.: Global and local behavior of positive solutions of nonlinear elliptic equations. Commun. Pure Appl. Math.4, 525-598 (1981) · Zbl 0465.35003 · doi:10.1002/cpa.3160340406 [3] Jaffe, A., Taubes, C.: Vortices and monopoles. Progress in Physics 2. Boston: Birkhäusen 1980 · Zbl 0457.53034 [4] Parker, T. Gauge theories on four dimensional manifolds. Commun. Math. Phys.85, 563-602 (1982) · Zbl 0502.53022 · doi:10.1007/BF01403505 [5] Sibner, L.M.: Removable singularities of Yang-Mills fields inR 3. Compositio Math.53, 91-104 (1984) · Zbl 0552.58037 [6] Sibner, L.M., Sibner, R.J.: Removable singularities of coupled Yang-Mills fields inR 3. Commun. Math. Phys.93, 1-17 (1984) · Zbl 0552.35028 · doi:10.1007/BF01218636 [7] Smith, P.D.: In preparation [8] Uhlenbeck, K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83, 11-29 (1982) · Zbl 0491.58032 · doi:10.1007/BF01947068 [9] Uhlenbeck, K.: Connections withL P bounds on curvature. Commun. Math. Phys.83, 31-42 (1982) · Zbl 0499.58019 · doi:10.1007/BF01947069
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.