双曲空间上p(x)-Laplace算子的Picone恒等式及其应用
A Picone's identity for the p(x)-Laplace operator on hyperbolic space
刘娜 1余路娟1
作者信息
- 1. 华北水利水电大学 数学与统计学院,河南 郑州 450046
- 折叠
摘要
Picone恒等式在偏微分方程的研究中起着重要的作用,其应用非常广泛.把欧式空间RN中的p(x)-Laplace算子推广到双曲球模型BN和双曲半模型HN上,建立双曲空间上p(x)-Laplace算子相对应的Picone恒等式并给出这些恒等式的应用,从而把欧氏空间中变指数问题的相关结果推广到双曲空间上.
Abstract
Picone's identity plays a crucial role in the study of partial differential equations,and its applications are very extensive.In this paper,we extend the p(x)-Laplace operator from Euclidean space to hyperbolic space,including both the ball model BN and the half space model HN.We establish Picones identities corresponding to the p(x)-Laplace opera-tor on hyperbolic space and provide applications for these identities.Therefore,the relevant results of the variable exponents problem in Euclidean space can be generalized to hyperbolic space.
关键词
Picone恒等式/p(x)-Laplace算子/双曲空间Key words
Picone's identity/p(x)-Laplace operator/hyperbolic space引用本文复制引用
出版年
2024
NETL
NSTL
万方数据