Elliptic systems and material interpenetration

Details Elliptic systems and material interpenetration Elliptic systems and material interpenetration

2008-05-31

arxiv.org/abs/0806.0066v1

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

Mathematics

Analysis of PDEs

10 pages, two figures, submitted

Scientific paper

We classify the second order, linear, two by two systems for which the two fundamental theorems for planar harmonic mappings, the Rado'-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 the same operator on both diagonal blocks. In particular, we prove that the aforementioned Theorems cannot be extended to solutions of either the Lame' system of elasticity, or of elliptic systems in diagonal form, even with just slightly different operators for the two components.

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