Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces | Zendy

Piotr Hajłasz | Zendy

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Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces

Author(s) -

Piotr Hajłasz

Publication year - 2008

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/s00208-008-0291-7

Subject(s) - mathematics , lipschitz continuity , sobolev space , class (philosophy) , pure mathematics , integer (computer science) , metric space , polyhedron , metric (unit) , combinatorics , operations management , artificial intelligence , computer science , economics , programming language

We prove that Lipschitz mappings are dense in the Newtonian–Sobolev classes N 1,p (X, Y) of mappings from spaces X supporting p-Poincaré inequalities into a finite Lipschitz polyhedron Y if and only if Y is [p]-connected, π 1(Y) = π 2(Y) = · · · = π [p](Y) = 0, where [p] is the largest integer less than or equal to p.

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