Quantitative estimates on Jacobians for hybrid inverse problems

2015/01/13 by Giovanni Alessandrini, Vincenzo Nesi, Alessandrini, Giovanni +1
Computer Science · Engineering · Mathematics · #30C62 #35J55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems #math.AP #msc:30C62 #msc:35J55

paper · pdf · doi:10.48550/arxiv.1501.03005

15 pages, submitted

arxiv created 2015/01/13 · openalex publication_date 2015/01/13 · arxiv updated 2015/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider σ-harmonic mappings, that is mappings U whose components u_i solve a divergence structure elliptic equation \rm div (σ∇ u_i)=0, for i=1,…,n . We investigate whether, with suitably prescribed Dirichlet data, the Jacobian determinant can be bounded away from zero. Results of this sort are required in the treatment of the so-called hybrid inverse problems, and also in the field of homogenization studying bounds for the effective properties of composite materials.

Citations

• Estimates for the dilatation of σ-harmonic mappings

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