TY - JOUR
T1 - Weak limits of Sobolev homeomorphisms are one to one almost everywhere
AU - Bouchala, Ondřej
AU - Hencl, Stanislav
AU - Zhu, Zheng
N1 - Publisher Copyright:
© The Author(s) 2025.
PY - 2025/7
Y1 - 2025/7
N2 - We prove that the key property in models of Nonlinear Elasticity which corresponds to the non-interpenetration of matter, i.e. injectivity a.e., can be achieved in the class of weak limits of homeomorphisms under very minimal assumptions. Let Ω⊂Rn be a domain and let p>n2 for n≥4 or p≥1 for n=2,3. Assume that fk∈W1,p is a sequence of homeomorphisms such that fk⇀f weakly in W1,p and assume that Jf>0 a.e. Then we show that f is injective a.e.
AB - We prove that the key property in models of Nonlinear Elasticity which corresponds to the non-interpenetration of matter, i.e. injectivity a.e., can be achieved in the class of weak limits of homeomorphisms under very minimal assumptions. Let Ω⊂Rn be a domain and let p>n2 for n≥4 or p≥1 for n=2,3. Assume that fk∈W1,p is a sequence of homeomorphisms such that fk⇀f weakly in W1,p and assume that Jf>0 a.e. Then we show that f is injective a.e.
UR - https://www.scopus.com/pages/publications/105007473844
U2 - 10.1007/s00526-025-03041-2
DO - 10.1007/s00526-025-03041-2
M3 - 文章
AN - SCOPUS:105007473844
SN - 0944-2669
VL - 64
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 6
M1 - 186
ER -