变指数Laplace算子的Liouville型定理

华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (1): 84-93.

变指数Laplace算子的Liouville型定理

王林峰

南通大学，理学院, 江苏，南通 226000

收稿日期:2007-12-07 修回日期:2008-02-15 出版日期:2009-01-25 发布日期:2009-01-25
通讯作者: 王林峰

Liouville theorem about the variable exponent Laplacian(Chinese)

Wang Lin-feng

School of Science, Nantong University, Nantong, Jiangsu 226000, China

Received:2007-12-07 Revised:2008-02-15 Online:2009-01-25 Published:2009-01-25
Contact: Wang Lin-feng

摘要/Abstract

摘要：

设$(M, \mathrm{g})$~%
是带度量~$\mathrm{g}$~的~$n$~维黎曼流形, $p(x)>1$~是~$M$~上的
~$\mathrm{C}^1$~光滑函数, 本文证明了在一定的体积增长的条件下,
$M$~上关于变指数~Laplace~算子
~$\mathrm{div}(|\nabla u|^{p(x)-2}\nabla )$~%
的弱极大值原理, 并利用该极大值原理证明了相应于变指数~Laplace~算子的
~Liouville~型定理.

关键词: 变指数 Laplace, Liouville型定理, 体积增长, 变指数 Laplace, Liouville型定理, 体积增长

Abstract:

A weak maximum principle for the variable exponent Laplace
on a complete noncompact Riemannian manifold under suitable
conditions about the growth of the volume was established, by which
a Liouville type theorem for the variable exponent Laplace was
proved.

Key words: Liouville type theorem, growth of the volume, variable exponent Laplace, Liouville type theorem, growth of the volume

中图分类号:

O186

王林峰. 变指数Laplace算子的Liouville型定理[J]. 华东师范大学学报(自然科学版), 2009, 2009(1): 84-93.

Wang Lin-feng. Liouville theorem about the variable exponent Laplacian(Chinese)[J]. Journal of East China Normal University(Natural Sc, 2009, 2009(1): 84-93.