TY - JOUR

T1 - Nonlinear elliptic equation arising from gauge field theory and cosmology

AU - Chen, Xinfu

AU - Hastings, Stuart

AU - McLeod, J. Bryce

AU - Yang, Yisong

PY - 1994

Y1 - 1994

N2 - We study radially symmetric solutions of a nonlinear elliptic partial differential equation in R2 with critical Sobolev growth, i.e. the nonlinearity is of exponential type. This problem arises from a wide variety of important areas in theoretical physics including superconductivity and cosmology. Our results lead to many interesting implications for the physical problems considered. For example, for the self-dual Chern-Simons theory, we are able to conclude that the electric charge, magnetic flux, or energy of a non-topological N-vortex solution may assume any prescribed value above an explicit lower bound. For the Einstein-matter-gauge equations, we find a necessary and sufficient condition for the existence of a self-dual cosmic string solution. Such a condition imposes an obstruction for the winding number of a string in terms of the universal gravitational constant.

AB - We study radially symmetric solutions of a nonlinear elliptic partial differential equation in R2 with critical Sobolev growth, i.e. the nonlinearity is of exponential type. This problem arises from a wide variety of important areas in theoretical physics including superconductivity and cosmology. Our results lead to many interesting implications for the physical problems considered. For example, for the self-dual Chern-Simons theory, we are able to conclude that the electric charge, magnetic flux, or energy of a non-topological N-vortex solution may assume any prescribed value above an explicit lower bound. For the Einstein-matter-gauge equations, we find a necessary and sufficient condition for the existence of a self-dual cosmic string solution. Such a condition imposes an obstruction for the winding number of a string in terms of the universal gravitational constant.

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U2 - 10.1098/rspa.1994.0115

DO - 10.1098/rspa.1994.0115

M3 - Article

AN - SCOPUS:0028768496

VL - 446

SP - 453

EP - 478

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 1928

ER -