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.

Elliptic systems and material interpenetration / Giovanni, Alessandrini; Nesi, Vincenzo. - In: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI. - ISSN 0208-6573. - 40:1(2009), pp. 105-115. [10.7169/facm/1238418801]

Elliptic systems and material interpenetration

NESI, Vincenzo
2009

Abstract

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.
2009
01 Pubblicazione su rivista::01a Articolo in rivista
Elliptic systems and material interpenetration / Giovanni, Alessandrini; Nesi, Vincenzo. - In: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI. - ISSN 0208-6573. - 40:1(2009), pp. 105-115. [10.7169/facm/1238418801]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/70681
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