Global Integrability of the Reciprocal of Jacobians for Homeomorphisms of Finite Distortion

2025/12/17 by Doležalová, Anna, Onninen, Jani, Zhu, Yizhe +1
#46E35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.15519

Abstract

For a homeomorphism with p-integrable distortion, we obtain the optimal global degree of integrability for the reciprocal of its Jacobian determinant. As an application, we strengthen the result of Doležalová, Hencl and Malý concerning weak limits of Sobolev homeomorphisms with finite distortion. Such limits represent physically admissible deformations, as they remain injective almost everywhere and thus adhere as closely as possible to the principle of non-interpenetration of matter in mathematical models of nonlinear elasticity.

Citations

• Lower semicontinuity, Stoilow factorization and principal maps
• Sobolev homeomorphic extensions from two to three dimensions
• On the lack of compactness in the axisymmetric neo-Hookean model
• The Sobolev Jordan-Schonflies Problem
• Sobolev homeomorphic extensions onto John domains
• Monotone Hopf-Harmonics
• Sobolev homeomorphic extensions
• The closure of planar diffeomorphisms in Sobolev spaces
• Smoothed Projections and Mixed Boundary Conditions
• The coarea formula for Sobolev mappings
• Quasiconformal maps in metric spaces with controlled geometry
• Convexity conditions and existence theorems in nonlinear elasticity

Related

• Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity
• On equicontinuity of homeomorphisms with finite distortion in the plane
• Extension of boundary homeomorphisms to mappings of finite distortion
• Foward the theory of Sobolev's mappings on the plane
• Weak limits of Sobolev homeomorphisms are one to one