Improved existence results of solutions to the gravitational Maxwell gauged $O(3)$ sigma model
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Abstract:
We improve the existence result of finite energy solutions to the self-dual equations of the gravitational Maxwell gauged $O(3)$ sigma model in $(2+1)$-dimensional Minkowski space for arbitrary location of strings for a small gravitational constant using the standard super- and subsolution method. We construct an explicit supersolution and use the weighted Sobolev space for a subsolution.References
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Additional Information
- Kyungwoo Song
- Affiliation: Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
- Email: kyusong@khu.ac.kr
- Received by editor(s): July 14, 2015
- Received by editor(s) in revised form: September 21, 2015
- Published electronically: December 22, 2015
- Communicated by: Joachim Krieger
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3499-3505
- MSC (2010): Primary 81T13, 35B40, 35J61
- DOI: https://doi.org/10.1090/proc/12967
- MathSciNet review: 3503717