Advances in Differential Equations
- Adv. Differential Equations
- Volume 5, Number 1-3 (2000), 369-400.
A variational problem for manifold valued functions
We prove a result of existence and multiplicity for local minima of a functional defined on maps from $\mathbb R^3$ to a compact Riemannian manifold $\mathcal M$. The interest in such a minimization problem lies in possible applications to field theory. Namely, the solutions to our variational problem are related to the existence of topological solitons.
Adv. Differential Equations, Volume 5, Number 1-3 (2000), 369-400.
First available in Project Euclid: 27 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
Secondary: 35J20: Variational methods for second-order elliptic equations 49J10: Free problems in two or more independent variables
Benci, Vieri; Giannoni, Fabio; Piccione, Paolo. A variational problem for manifold valued functions. Adv. Differential Equations 5 (2000), no. 1-3, 369--400. https://projecteuclid.org/euclid.ade/1356651389