Mappings with Integrable Dilatation in Higher Dimensions
نویسندگان
چکیده
Let F ∈ W 1 , n loc (Ω ; R ) be a mapping with nonnegative Jacobian JF (x) = detDF (x) ≥ 0 for a.e. x in a domain Ω ⊂ R n . The dilatation of F is defined (almost everywhere in Ω) by the formula K(x) = |DF (x)| JF (x) · Iwaniec and Šverák [IS] have conjectured that if p ≥ n − 1 and K ∈ Lploc(Ω) then F must be continuous, discrete and open. Moreover, they have confirmed this conjecture in the two-dimensional case n = 2 . In this article, we verify it in the higher-dimensional case n ≥ 2 whenever p > n − 1 .
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