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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.

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