Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$

Details Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$ Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$

2011-02-11

arxiv.org/abs/1102.2462v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ which
vanishes to infinite order at the origin, and such that the ratio of the norm
of the $\bar z$ derivative to the norm of the $z$ derivative also vanishes to
infinite order. This gives a counterexample to strong unique continuation for a
vector valued analogue of the Beltrami equation.

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