Jacobian of weak limits of Sobolev homeomorphisms
Hencl, S., & Onninen, J. (2018). Jacobian of weak limits of Sobolev homeomorphisms. Advances in Calculus of Variations, 11 (1), 65-73. doi:10.1515/acv-2016-0005
Published inAdvances in Calculus of Variations
© 2018 Walter de Gruyter GmbH. Published in this repository with the kind permission of the publisher.
Let Ω be a domain in Rn, where n=2,3. Suppose that a sequence of Sobolev homeomorphisms fk:Ω→Rn with positive Jacobian determinants, J(x,fk)>0, converges weakly in W1,p(Ω,Rn), for some p⩾1, to a mapping f. We show that J(x,f)⩾0 a.e. in Ω. Generalizations to higher dimensions are also given.