Approximation of sobolev mappings
✍ Scribed by Piotr HajŁasz
- Book ID
- 107967660
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 994 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0362-546X
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## Abstract We establish a necessary and sufficient topological condition for maps that are in __W__^1,__p__^(__M, N__) to be connected by continuous paths in __W__^1,__p__^(__M, N__) to maps in __W__^1,__q__^(__M, N__), __q__ > __q__ ≥ 1. We also obtain a necessary and sufficient topological condi
We show that each quasi-light mapping fin the Sobolev space W~'n(s R n) satisfying ]Df(x)ln<=K(x,f)J(x,f) for almost every x and for some K~Lr(s r > n-1, is open and discrete. The assumption that f be quasilight can be dropped if, in addition, it is required that f~ WI'P(f2, R n) for some p \_\_\_ n