# Some issues on the p-Laplace equation in cylindrical domains - Zurich Open Repository and Archive

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 ${\Omega_\infty = \Bbb{R}^q \times \omega}$.

## 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 ${\Omega_\infty = \Bbb{R}^q \times \omega}$.

## Altmetrics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2008 25 Nov 2009 10:24 05 Apr 2016 13:31 Trudy Matematicheskogo Instituta 0371-9685 https://doi.org/10.1134/S0081543808020235 http://www.ams.org/mathscinet-getitem?mr=2489714