Asymptotics of Sobolev embeddings and singular perturbations for the <IMG >-Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Asymptotics of Sobolev embeddings and singular perturbations for the -Laplacian

Authors:

Affiliation:

Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMR2071 CNRS-UChile), Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile ; Departamento de Matemáticas, FCFM Universidad de Concepción, Casilla 160-C, Concepción, Chile

Abstract:

We consider the best constant

for the embedding of $W^{1,p} (Omega_lambda)$ into

where

. Here

with

a smooth, bounded domain in $mathbb{R} ^n$ and

a large positive number. It is proven by the validity of the expansion

$begin{displaymath}S( Omega_lambda) = S(mathbb{R} ^n_+) - lambda^{-1} gamma max_{xin partial Omega} H(x) + o ( lambda^{-1} ), nonumberend{displaymath}$

, where

is a positive constant depending on

and

. The behavior of associated extremals, which satisfy an equation involving the

-Laplacian operator, is also analyzed.

Keywords:

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