Quantitative Estimates on Jacobians for Hybrid Inverse Problems
Giovanni Alessandrini, Vincenzo Nesi · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · 2015
We consider σ-harmonic mappings, that is mappings U whose components u i solve a divergence structure elliptic equation 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 eld of homogenization studying bounds for the eective properties of composite materials.