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A linear boundary value problem for weakly quasiregular mappings in space. (English summary) Calc. Var. Partial Differential Equations 13 (2001), no. 3, 295–310. Given L ≥ 1 and a domain Ω ⊂ Rn, n ≥ 3, a map u: Ω → Rn in W 1,p loc (Ω) is called weakly L-quasiregular (qr) if |Du(x) | n ≤ L det Du(x) holds a.e. in Ω. The author proves that there exists p < n such that a weakly qr map can only assume linear boundary values. On the other hand, it is shown that for all L ≥ 1 and 1 ≤ p < nL L+1 every linear map can be the boundary value of a weakly L-qr map

Year: 2013

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