Communications in Analysis and Geometry

Volume 13 (2005)

Number 5

On the weak limits of smooth maps for the Dirichlet energy between manifold

Pages: 929 – 938



Fengbo Hang


We identify all the weak sequential limits of smooth maps in $W^{1,2}\left( M,N\right) $. In particular, this implies a necessary and sufficient topological condition for smooth maps to be weakly sequentially dense in $W^{1,2}\left( M,N\right) $.

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