In this paper we consider a model introduced in [3] which describes the interaction between the matter and the electromagnetic field from a unitarian standpoint. This model is based on a semilinear perturbation of the Maxwell equations and, in the magnetostatic case, reduces to the following nonlinear elliptic degenerate equation: ∇×(∇×A)=W′(|A|^2)A, where "∇×" is the curl operator, W:R→R is a suitable nonlinear term, and A:R^3→R^3 is the gauge potential associated with the magnetic field H. We prove the existence of a nontrivial finite energy solution with a kind of cylindrical symmetry. The proof is carried out by using a suitable variational framework based on the Hodge decomposition, which is crucial in order to handle the strong degeneracy of the equation. Moreover, the use of a natural constraint and a concentration-compactness argument are also required.

D'Aprile, T.c., Siciliano, G. (2011). Magnetostatic solutions for a semilinear perturbation of the Maxwell equations. ADVANCES IN DIFFERENTIAL EQUATIONS, 16(5/6), 435-466.

Magnetostatic solutions for a semilinear perturbation of the Maxwell equations

D'APRILE, TERESA CARMEN;
2011-01-01

Abstract

In this paper we consider a model introduced in [3] which describes the interaction between the matter and the electromagnetic field from a unitarian standpoint. This model is based on a semilinear perturbation of the Maxwell equations and, in the magnetostatic case, reduces to the following nonlinear elliptic degenerate equation: ∇×(∇×A)=W′(|A|^2)A, where "∇×" is the curl operator, W:R→R is a suitable nonlinear term, and A:R^3→R^3 is the gauge potential associated with the magnetic field H. We prove the existence of a nontrivial finite energy solution with a kind of cylindrical symmetry. The proof is carried out by using a suitable variational framework based on the Hodge decomposition, which is crucial in order to handle the strong degeneracy of the equation. Moreover, the use of a natural constraint and a concentration-compactness argument are also required.
2011
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
D'Aprile, T.c., Siciliano, G. (2011). Magnetostatic solutions for a semilinear perturbation of the Maxwell equations. ADVANCES IN DIFFERENTIAL EQUATIONS, 16(5/6), 435-466.
D'Aprile, Tc; Siciliano, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/102827
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