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.
PublisherWalter de Gruyter GmbH
MetadataShow full item record
Showing items with similar title or keywords.
Hencl, Stanislav; Onninen, Jani (Walter de Gruyter GmbH, 2018)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 ...
Introducing Golden Section in the Mathematics Class to Develop Critical Thinking from the STEAM Perspective Dana-Picard, Thierry; Hershkovitz, Sara; Lavicza, Zsolt; Fenyvesi, Kristof (SEAMEO STEM-ED, 2021)The Golden Section is a mathematical concept that is one of the most famous examples of connections between mathematics and the arts. Despite its widespread references in various areas of nature, art, architecture, literature, ...
Campbell, D.; Hencl, S.; Tengvall, Ville (Elsevier Inc., 2018)Let Ω ⊂ R n, n ≥ 4, be a domain and 1 ≤ p < [n/2], where [a] stands for the integer part of a. We construct a homeomorphism f ∈ W1,p((−1, 1)n, R n) such that Jf = det Df > 0 on a set of positive measure and Jf < 0 on a set ...
Di Marino, Simone; Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios (Springer, 2021)We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space ...
Lähdesmäki, Tuuli (Birkhäuser, 2017)Since the 1920s and 1930s, constructivist and concretist visual art movements have stressed geometric forms, proportions and orders as a base for artistic expressions and aesthetic experiences. After the World War II ...