Calculus of Variations and Geometric Measure Theory

M. Giaquinta - D. Mucci

Density results for the $ W^{1/2}$ energy of maps into a manifold

created on 06 Apr 2004
modified by mucci on 21 Nov 2005


Published Paper

Inserted: 6 apr 2004
Last Updated: 21 nov 2005

Journal: Mathematische Zeitschrift
Volume: 251
Pages: 535-549
Year: 2005



We show that maps from $B^n$ to a smooth compact boundaryless manifold ${\cal Y}$ which are smooth out of a singular set of dimension $n-2$ are dense for the strong topology in $W^{1/2}(B^n,{\cal Y})$. We also prove that for $n{\geq} 2$ smooth maps from $B^n$ to ${\cal Y}$ are dense in $W^{1/2}(B^n,{\cal Y})$ if and only if \,${\pi}_1({\cal Y})=0$, i.e. the first homotopy group of ${\cal Y}$ is trivial.