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If  M  is a compact smooth manifold and  X  is a compact metric space, then the Sobolev space  W  1, p  ( M , X ) is defined through an isometric embedding of  X  into a Banach space. We prove that the answer to the question whether Lipschitz mappings  Lip  ( M , X ) are dense in  W  1, p  ( M , X ) may depend on the isometric embedding of the target.

Sobolev Mappings: Lipschitz Density is not an Isometric Invariant of the Target