Functiones et Approximatio Commentarii Mathematici

Elliptic systems and material interpenetration

Giovanni Alessandrini and Vincenzo Nesi

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We classify the second order, linear, two by two systems for which the two fundamental theorems for planar harmonic mappings, the Radó--Kneser--Choquet theorem and the H. Lewy theorem, hold. They are those which, up to a linear change of variable, can be written in diagonal form with \emph{the same} operator on both diagonal blocks. In particular, we prove that the aforementioned theorems cannot be extended to solutions of either the Lamé system of elasticity, or of elliptic systems in diagonal form, even with just slightly different operators for the two components.

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Funct. Approx. Comment. Math., Volume 40, Number 1 (2009), 105-115.

First available in Project Euclid: 30 March 2009

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Zentralblatt MATH identifier

Primary: 31A05: Harmonic, subharmonic, superharmonic functions
Secondary: 35J25: Boundary value problems for second-order elliptic equations 30C60 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Harmonic mappings univalence


Alessandrini, Giovanni; Nesi, Vincenzo. Elliptic systems and material interpenetration. Funct. Approx. Comment. Math. 40 (2009), no. 1, 105--115. doi:10.7169/facm/1238418801.

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