分数阶p-Laplace方程解的单调性公式
Monotonicity formula for solutions of fractional p-Laplace equations
王琦 1沃维丰1
作者信息
- 1. 宁波大学数学与统计学院,浙江宁波 315211
- 折叠
摘要
研究了分数阶p-Laplace方程解的单调性公式.基于Caffarelli-Silverstre的延拓技术,将分数阶p-Laplace方程相应的扩展问题表述为半空间中一个退化或奇异局部方程.通过建立与扩展问题相关的Almgren型频率函数,结合散度定理和积分估计获得了延拓函数的单调性公式.
Abstract
In this paper,we study the monotonicity formula of solutions for fractional p-Laplace equations.Based on the extension technique of Caffarelli-Silverstre,the corresponding extension problem of fractional p-Laplace equation is addressed as a degenerate or singular local equation in half space.By establishing the Almgren-type frequency function related to the extended problem,and combining the divergence theorem and integral estimation,the monotonicity formula of the extended function is obtained.
关键词
分数阶p-Laplace方程/延拓技术/频率函数/单调性Key words
fractional p-Laplace/extension technology/frequency function/monotonicity引用本文复制引用
基金项目
国家自然科学基金(12271276)
浙江省自然科学基金(LY20A010011)
出版年
2024
NETL
NSTL
维普
万方数据