Elliptic systems and material interpenetration
Giovanni Alessandrini and Vincenzo Nesi
Source: Funct. Approx. Comment. Math. Volume 40, Number 1
(2009), 105-115.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.facm/1238418801
Mathematical Reviews number (MathSciNet): MR2527631
Zentralblatt MATH identifier: 05620888
Digital Object Identifier: doi:10.7169/facm/1238418801
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Functiones et Approximatio Commentarii Mathematici
