Lower Bounds for the Energy of Unit Vector Fields and Applications: Volume 152, Number 2 (1998), pages 379–403

✍ Scribed by Etienne Sandier

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 29 KB
• Volume: 171
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1999.3530

✦ Synopsis

A mistake in the proof of Theorem 1 occurred which was pointed out to the author by Tristan RivieÁ re. It is stated there that the constant C depends only on the domain and the H 1Â2 norm of the boundary data. It really should be the H s -norm for some s>1Â2 for the result to be correct.

The problem is the extension procedure described on p. 389. When g # H 1Â2 , the extension is possible but the energy of the extension cannot be controlled by the H 1Â2 norm.

This change to Theorem 1 should also be made in Theorem 1", where the H nÂ(n&1) norm should be replaced with the W s, n norm, for some s>1&1Ân, and in Theorems 2 and 3, where the H 1Â2 norm should be replaced with the H s norm, for some s>1Â2.