TITLE

Rotationally symmetric 1-harmonic maps from D 2 to S 2

AUTHOR(S)
dal Passo, Roberta; Giacomelli, Lorenzo; Moll, Salvador
PUB. DATE
August 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Aug2008, Vol. 32 Issue 4, p533
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider rotationally symmetric 1-harmonic maps from D 2 to S 2 subject to Dirichlet boundary conditions. We prove that the corresponding energy—a degenerate non-convex functional with linear growth—admits a unique minimizer, and that the minimizer is smooth in the bulk and continuously differentiable up to the boundary. We also show that, in contrast with 2-harmonic maps, a range of boundary data exists such that the energy admits more than one smooth critical point: more precisely, we prove that the corresponding Euler–Lagrange equation admits a unique (up to scaling and symmetries) global solution, which turns out to be oscillating, and we characterize the minimizer and the smooth critical points of the energy as the monotone, respectively non-monotone, branches of such solution.
ACCESSION #
31998857

 

Related Articles

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics