Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity

2017/04/26 by Anastasia Molchanova, Molchanova, A. O., S. K. Vodopyanov +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1704.08022

openalex publication_date 2017/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a sufficient condition for the weak limit of a sequence of W¹_q-homeomorphisms with finite distortion to be almost everywhere injective for q ≥ n-1, can be stated by means of composition operators. Applying this result, we study nonlinear elasticity problems with respect to these new classes of mappings. Furthermore, we impose loose growth conditions on the stored-energy function for the class of W¹_n-homeomorphisms with finite distortion and integrable inner as well as outer distortion coefficients.

Citations

• n-Harmonic mappings between annuli
• Convexity conditions and existence theorems in nonlinear elasticity

Cited by

• Reshetnyak-class mappings and composition operators

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