We consider σ-harmonic mappings, that is mappings U whose components ui solve a divergence structure elliptic equation div(σ∇ui) = 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.
Quantitative estimates on jacobians for hybrid inverse problems / Alessandrini, G.; Nesi, Vincenzo. - In: VESTNIK UZNO-URALʹSKOGO GOSUDARSTVENNOGO UNIVERSITETA. SERIA, MATEMATICESKOE MODELIROVANIE I PROGRAMMIROVANIE. - ISSN 2308-0256. - STAMPA. - 8:3(2015), pp. 25-41. [10.14529/mmp150302]
Quantitative estimates on jacobians for hybrid inverse problems
NESI, Vincenzo
2015
Abstract
We consider σ-harmonic mappings, that is mappings U whose components ui solve a divergence structure elliptic equation div(σ∇ui) = 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.| File | Dimensione | Formato | |
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