分数阶p-Laplace方程解的单调性公式

Monotonicity formula for solutions of fractional p-Laplace equations

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.