分数阶p-Laplace方程解的单调性公式
PDF下载 (196)王 琦,沃维丰.分数阶p-Laplace方程解的单调性公式[J].宁波大学学报(理工版),2024,37(1):38-42.DOI:10.20098/j.cnki.1001-5132.2023.0721
WANG Qi,WO Weifeng.Monotonicity formula for solutions of fractional p-Laplace equations[J].Journal of Ningbo University(Natural Science & Engineering Edition),2024,37(1):38-42.DOI:10.20098/j.cnki.1001-5132.2023.0721
| Title: | Monotonicity formula for solutions of fractional p-Laplace equations |
| 作者: | 王 琦, 沃维丰 |
| Author(s): | WANG Qi, WO Weifeng |
| 关键词: | 分数阶p-Laplace方程; 延拓技术; 频率函数; 单调性 |
| Keywords: | fractional p-Laplace; extension technology; frequency function; monotonicity |
| 分类号: | O175.25 |
| DOI: | 10.20098/j.cnki.1001-5132.2023.0721 |
| 文献标识码: | A |
| 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. |
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| 备注/Memo: | 收稿日期: 2023－07－27. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（12271276）; 浙江省自然科学基金（LY20A010011）. 第一作者: 王琦, 硕士研究生, 主要研究方向: 偏微分方程. E-mail: 3289666171@qq.com* 通信作者: 沃维丰, 博士/副教授, 主要研究方向: 偏微分方程. E-mail: woweifeng@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
