Planar ACL-homeomorphisms : Critical points of their components

Pages: 1391 - 1397, Volume 9, Issue 5, September 2010

doi:10.3934/cpaa.2010.9.1391       Abstract        Full Text (137.3K)       Related Articles

Gioconda Moscariello - Dipartimento di Matematica e Appl. “R. Caccioppoli”, Via Cintia- Monte S.Angelo, 80126 Napoli, Italy (email)
Antonia Passarelli di Napoli - Dipartimento di Matematica e Appl. “R. Caccioppoli”, Via Cintia- Monte S.Angelo, 80126 Napoli, Italy (email)
Carlo Sbordone - Dipartimento di Matematica e Appl. “R. Caccioppoli”, Via Cintia- Monte S.Angelo, 80126 Napoli, Italy (email)

Abstract: We study planar homeomorphisms $f: \Omega\subset R^2 $ onto $\to \Omega' \subset R^2$, $f=(u,v)$, which are absolutely continuous on lines parallel to the axes (ACL) together with their inverse $f^{-1}$. The main result is that $u$ and $v$ have almost everywhere the same critical points. This generalizes a previous result ([6]) concerning bisobolev mappings. Moreover we construct an example of a planar ACL-homeomorphism not belonging to the Sobolev class $W_{l o c}^{1,1}$.

Keywords:  ACL-homeomorphisms, mappings of finite distortion.
Mathematics Subject Classification:  Primary: 49N15, 49N60; Secondary: 46E35.

Received: September 2009;      Revised: October 2009;      Published: May 2010.