We study uniqueness of weak solutions of elliptic equations of the type

- div (a(x,u,∇u))+b(x,u)=f(x)

in a bounded domain Ω⊂ℝ n with Lipschitz boundary γ=∂Ω. We consider in particular mixed boundary conditions - i.e. Dirichlet condition on one part of the boundary and Neumann condition on the other part. A model equation could be

- div (a(x,u)|∇u|p(x)-2∇u)+b(x,u)=f(x),x∈Ω·

We establish uniqueness results for these equations. We also indicate conditions which guarantee existence of solution.

Antontsev, S; Chipot, M; Xie, Y (2007). *Uniqueness results for equations of the p(x)-Laplacian type.* Advances in Mathematical Sciences and Applications, 17(1):287-304.

## Abstract

We study uniqueness of weak solutions of elliptic equations of the type

- div (a(x,u,∇u))+b(x,u)=f(x)

in a bounded domain Ω⊂ℝ n with Lipschitz boundary γ=∂Ω. We consider in particular mixed boundary conditions - i.e. Dirichlet condition on one part of the boundary and Neumann condition on the other part. A model equation could be

- div (a(x,u)|∇u|p(x)-2∇u)+b(x,u)=f(x),x∈Ω·

We establish uniqueness results for these equations. We also indicate conditions which guarantee existence of solution.

## Citations

## 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: | 2007 |

Deposited On: | 11 Nov 2009 15:35 |

Last Modified: | 05 Apr 2016 13:23 |

Publisher: | Gakko Tosho |

ISSN: | 1343-4373 |

Official URL: | http://www1.gifu-u.ac.jp/~aiki/AMSA/vol17.html |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2337380 |

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