Chipot, M.; Sideris, T. On the Abelian Higgs model. (English) Zbl 0703.35031 Z. Angew. Math. Phys. 41, No. 1, 105-113 (1990). A proof of global existence for the time independent Abelian Higgs model is given. The problem is reduced to a nonlinear elliptic system in \({\mathbb{R}}^ 3\) of the form \[ -\Delta u+a^ 2u=f(u,v)+j(x),\quad -\Delta v+b^ 2v=g(u,v),\quad a=const,\quad b=const, \] where f and g are smooth functions and j is a quantity involving \(\delta\) functions of \(x=(x_ 1,x_ 2,x_ 3)\). Under relevant assumptions a solution (in distributional sense) with prescribed asymptotics near infinity is found. Reviewer: T.G.Genchev MSC: 35D05 Existence of generalized solutions of PDE (MSC2000) 35J60 Nonlinear elliptic equations 81T08 Constructive quantum field theory Keywords:global existence; Abelian Higgs model; nonlinear elliptic × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Adler, S. L. and T. Piran,Relaxation methods for gauge field equilibrium equations. Rev. Modern Phys.56, 1-40 (1984). · doi:10.1103/RevModPhys.56.1 [2] Bernstein, J.,Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that. Rev. Modern Phys.46, 7-48 (1974). · doi:10.1103/RevModPhys.46.7 [3] Bleecker, D.,Gauge Theory and Variational Principles. Addison-Wesley 1981. · Zbl 0481.58002 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.