Note on injectivity in second-gradient Nonlinear Elasticity

2025/07/07 by Hencl, Stanislav, Mohanta, Kaushik
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.04938

Abstract

Let q>1, (1-(1)/(q))a≥ 1 and let Ω⊂ ℝ² be Lipschitz domain. We show that planar mappings in the second order Sobolev space f∈ W^2,q(Ω,ℝ²) with |J_f|^-a∈ L¹(Ω) are homeomorphism if they agree with a homeomorphism on the boundary. The condition (1-(1)/(q))a≥ 1 is sharp. We also have a new sharp result about the H^n-1 measure of the projection of the set \J_f=0\ in ℝⁿ.

Citations

• Injectivity in second-gradient Nonlinear Elasticity

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