Non-existence and uniqueness results

for boundary value problems

for Yang-Mills connections

Author:
Takeshi Isobe

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1737-1744

MSC (1991):
Primary 35J50, 58E15, 81T13

DOI:
https://doi.org/10.1090/S0002-9939-97-03804-5

MathSciNet review:
1376764

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Abstract | References | Similar Articles | Additional Information

Abstract: We show uniqueness results for the Dirichlet problem for Yang-Mills connections defined in -dimensional () star-shaped domains with flat boundary values. This result also shows the non-existence result for the Dirichlet problem in dimension 4, since in 4-dimension, there exist countably many connected components of connections with prescribed Dirichlet boundary value. We also show non-existence results for the Neumann problem. Examples of non-minimal Yang-Mills connections for the Dirichlet and the Neumann problems are also given.

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Additional Information

**Takeshi Isobe**

Affiliation:
Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan

Email:
isobe@math.titech.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-97-03804-5

Keywords:
Yang-Mills,
boundary value problems,
non-existence,
uniqueness

Received by editor(s):
December 8, 1995

Communicated by:
Ronald Stern

Article copyright:
© Copyright 1997
American Mathematical Society