分数阶p-Laplace方程解的单调性公式  

Monotonicity formula for solutions of fractional p-Laplace equations

作　　者：王琦[1] 沃维丰 WANG Qi;WO Weifeng(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2024年第1期38-42,共5页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(12271276);浙江省自然科学基金(LY20A010011)。

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.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 

分 类 号：O175.25[理学—数学]