Advances in Differential Equations

A variational problem for manifold valued functions

Vieri Benci, Fabio Giannoni, and Paolo Piccione

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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.

Article information

Adv. Differential Equations, Volume 5, Number 1-3 (2000), 369-400.

First available in Project Euclid: 27 December 2012

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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.

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