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Some issues on the p-Laplace equation in cylindrical domains


Chipot, M; Xie, Y (2008). Some issues on the p-Laplace equation in cylindrical domains. Matematicheskii Institut im. VA Steklova. Trudy, 261:293-300.

Abstract

In this article the authors prove a theorem regarding the convergence of solutions for the problems $$ \cases -\Delta_p u_l=f(X_2) &\text{ in $\Omega_l$},\\ u_l=0 &\text{ on $\partial \Omega_l$},\endcases $$ as $l\to \infty$. Here the $n$-dimensional space $\Bbb{R}^n$ is written as the product $\Bbb{R}^q\times \Bbb{R}^{n-q}$ and $X \in \Bbb{R}^n$ is written as $X = (X_1, X_2) = (x_1, \dots, x_q, x_{q+1}, \dots, x_n)$. The domain is $\Omega_l = (-l,l)^q \times \omega$ and $\omega$ is a smooth bounded domain in $\Bbb{R}^{n-q}$. The authors also present a Liouville-type nonexistence result on the domain ${\Omega_\infty = \Bbb{R}^q \times \omega}$.

In this article the authors prove a theorem regarding the convergence of solutions for the problems $$ \cases -\Delta_p u_l=f(X_2) &\text{ in $\Omega_l$},\\ u_l=0 &\text{ on $\partial \Omega_l$},\endcases $$ as $l\to \infty$. Here the $n$-dimensional space $\Bbb{R}^n$ is written as the product $\Bbb{R}^q\times \Bbb{R}^{n-q}$ and $X \in \Bbb{R}^n$ is written as $X = (X_1, X_2) = (x_1, \dots, x_q, x_{q+1}, \dots, x_n)$. The domain is $\Omega_l = (-l,l)^q \times \omega$ and $\omega$ is a smooth bounded domain in $\Bbb{R}^{n-q}$. The authors also present a Liouville-type nonexistence result on the domain ${\Omega_\infty = \Bbb{R}^q \times \omega}$.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:25 Nov 2009 10:24
Last Modified:05 Apr 2016 13:31
Publisher:Trudy Matematicheskogo Instituta
ISSN:0371-9685
Publisher DOI:https://doi.org/10.1134/S0081543808020235
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2489714

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