Asymptotics of Sobolev embeddings and singular perturbations for the -Laplacian

Authors:
Manuel del Pino and César Flores

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2931-2939

MSC (2000):
Primary 35J20; Secondary 35B40

DOI:
https://doi.org/10.1090/S0002-9939-02-06535-8

Published electronically:
April 10, 2002

MathSciNet review:
1908916

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the best constant for the embedding of into where , . Here with a smooth, bounded domain in and a large positive number. It is proven by the validity of the expansion

as , where is a positive constant depending on and . The behavior of associated extremals, which satisfy an equation involving the -Laplacian operator, is also analyzed.

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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

Email:
delpino@dim.uchile.cl

**César Flores**

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

Email:
cflores@dim.uchile.cl

DOI:
https://doi.org/10.1090/S0002-9939-02-06535-8

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