Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Superposition operator in Sobolev spaces on domains


Author: Denis A. Labutin
Journal: Proc. Amer. Math. Soc. 128 (2000), 3399-3403
MSC (1991): Primary 46E35; Secondary 47H30
Published electronically: May 11, 2000
MathSciNet review: 1676320
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For an arbitrary open set $\Omega\subset \mathbb{R}^n$ we characterize all functions $G$ on the real line such that $G\circ u\in W^{1,p}(\Omega)$ for all $u\in W^{1,p}(\Omega)$. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding $ {W^{1,p}(\Omega)\hookrightarrow L^\infty(\Omega)}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46E35, 47H30

Retrieve articles in all journals with MSC (1991): 46E35, 47H30


Additional Information

Denis A. Labutin
Affiliation: Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra 0200, ACT, Australia
Email: labutin@maths.anu.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05421-6
PII: S 0002-9939(00)05421-6
Keywords: Sobolev spaces, superposition operator
Received by editor(s): August 1, 1998
Received by editor(s) in revised form: January 22, 1999
Published electronically: May 11, 2000
Additional Notes: This work was supported by the Russian Foundation for Basic Research grant 96-01-00243.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society