A priori estimates of solutions to nonlinear fractional Laplacian equation
A priori estimates of solutions to nonlinear fractional Laplacian equation
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DOI：
10.3934/era.2023056
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发表时间：
2022
影响因子：
0.8
通讯作者：
Zhang Tao;Tingzhi Cheng
中科院分区：
文献类型：
--
作者：
Zhang Tao;Tingzhi Cheng
本文主要研究几类具有临界Sobolev指数的半线性分数阶Laplacian方程的先验估计。利用移动平面的方法，我们可以得到与非线性分数阶拉普拉斯方程解的存在性密切相关的先验估计。我们的结果可以将二阶椭圆型方程的先验估计推广到分数阶Laplacian方程，并且我们相信这里所用的方法将适用于更一般的非局部问题.
In this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent. Employing the method of moving planes, we can achieve a priori estimates which are closely connected to the existence of solutions to nonlinear fractional Laplacian equations. Our result can extend a priori estimates of the second order elliptic equation to the fractional Laplacian equation and we believe that the method used here will be applicable to more general nonlocal problems.