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Quantitative estimates on Jacobians for hybrid inverse problems. (English) Zbl 1341.31005
Summary: We consider \(\sigma\)-harmonic mappings, that is mappings \(U\) whose components \(u_i\) solve a divergence structure elliptic equation \(\mathrm{div}(\sigma\nabla u_i)=0\), for \(i=1,\ldots, n\). 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.

31C05 Harmonic, subharmonic, superharmonic functions on other spaces
35J57 Boundary value problems for second-order elliptic systems
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