Jacobians of Sobolev homeomorphisms

Hencl, Stanislav; Mal�, Jan
May 2010
Calculus of Variations & Partial Differential Equations;May2010, Vol. 38 Issue 1/2, p233
Academic Journal
Let O ? Rn be a domain.We show that each homeomorphism f in the Sobolev space W1,1loc (O,Rn) satisfies either Jf = 0 a.e or Jf = 0 a.e. if n = 2 or n = 3. For n > 3we prove the same conclusion under the stronger assumption that f ? W1,sloc (O,Rn) for some s > [n/2] (or in the setting of Lorentz spaces).


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