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

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

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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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