Volume 8, no. 3Pages 25 - 41

Quantitative Estimates on Jacobians for Hybrid Inverse Problems

G. Alessandrini, V. Nesi
We consider sigma-harmonic mappings, that is mappings U whose components u_i solve a divergence structure elliptic equation sigma nabla 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.
Full text
elliptic equations; Beltrami operators; hybrid inverse problems; composite materials.
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