Title

Smooth Counterexamples to Strong Unique Continuation for a Beltrami System in C2

Document Type

Article

Publication Date

2012

Publication Source

Communications in Partial Differential Equations

Volume

37

Issue

12

Inclusive pages

2228-2244

Publisher

Taylor & Francis

ISBN/ISSN

0360-5302

Peer Reviewed

yes

Abstract

We construct an example of a smooth map C to C2 which vanishes to infinite order at the origin, and such that the ratio of the norm of the z-bar 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.

Keywords

Elliptic Systems of Partial Differential Equations, Unique Continuation

Disciplines

Analysis | Mathematics