Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Asymptotics of Sobolev embeddings and singular perturbations for the $p$-Laplacian

Authors: Manuel del Pino and César Flores
Journal: Proc. Amer. Math. Soc. 130 (2002), 2931-2939
MSC (2000): Primary 35J20; Secondary 35B40
Published electronically: April 10, 2002
MathSciNet review: 1908916
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the best constant $S(\Omega_\lambda)$for the embedding of $W^{1,p} (\Omega_\lambda)$ into $L^q(\Omega_\lambda)$ where $1<p<2$, $p<q< {Np\over N-p}$. Here $\Omega_\lambda = \lambda \Omega$ with $\Omega$a smooth, bounded domain in $\mathbb{R} ^n$ and $\lambda$ a large positive number. It is proven by the validity of the expansion

\begin{displaymath}S( \Omega_\lambda) = S(\mathbb{R} ^n_+) - \lambda^{-1} \gamma \max_{x\in \partial \Omega} H(x) + o ( \lambda^{-1} ), \nonumber\end{displaymath}  

as $\lambda \to \infty$, where $\gamma$ is a positive constant depending on $p,q$ and $N$. The behavior of associated extremals, which satisfy an equation involving the $p$-Laplacian operator, is also analyzed.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J20, 35B40

Retrieve articles in all journals with MSC (2000): 35J20, 35B40

Additional Information

Manuel del Pino
Affiliation: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMR2071 CNRS-UChile), Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile

César Flores
Affiliation: Departamento de Matemáticas, FCFM Universidad de Concepción, Casilla 160-C, Concepción, Chile

PII: S 0002-9939(02)06535-8
Received by editor(s): May 1, 2001
Published electronically: April 10, 2002
Additional Notes: This work was supported by grants Fondecyt Lineas Complementarias 8000010, DIUC 200.015.015-1.0, ECOS/CONICYT, and FONDAP
Dedicated: To the memory of Carlos Cid
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia