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Improved existence results of solutions to the gravitational Maxwell gauged $ O(3)$ sigma model


Author: Kyungwoo Song
Journal: Proc. Amer. Math. Soc. 144 (2016), 3499-3505
MSC (2010): Primary 81T13, 35B40, 35J61
DOI: https://doi.org/10.1090/proc/12967
Published electronically: December 22, 2015
MathSciNet review: 3503717
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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.


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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

DOI: https://doi.org/10.1090/proc/12967
Keywords: The gravitational Maxwell gauged $O(3)$ sigma model, super- and subsolution method, weighted Sobolev space
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
Article copyright: © Copyright 2015 American Mathematical Society