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arXiv · 1501.03005

Quantitative estimates on Jacobians for hybrid inverse problems

Giovanni Alessandrini·Vincenzo Nesi
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Abstract

We consider $\sigma$-harmonic mappings, that is mappings $U$ whose components $u_i$ solve a divergence structure elliptic equation ${\rm div} (\sigma \nabla u_i)=0$, 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.

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Giovanni Alessandrini, Vincenzo Nesi. 2015-01-13. Quantitative estimates on Jacobians for hybrid inverse problems. https://arxiv.org/abs/1501.03005

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