The Fractional Laplacian
The Fractional Laplacian
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DOI：
10.1142/10550
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Wenxiong Chen;Yan Li;Pei-E Ma
中科院分区：
文献类型：
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作者：
Wenxiong Chen;Yan Li;Pei-E Ma
这是一本独特的书，提供了一个全面的了解非线性方程，涉及分数拉普拉斯算子以及其他非局部运营商。从分数拉普拉斯算子的定义出发，逐步将读者引向当前这一领域的研究前沿。解释和插图是足够基本的，使一年级的研究生可以很容易地遵循，而它是先进的，足以包括许多新的想法，方法和结果，最近出现在研究文献，研究人员会发现有帮助的。它着重介绍非局部问题的直接方法，而不经过推广，如移动平面的直接方法、移动球面的直接方法、直接爆破和重新标度的论点等，与大多数其他书籍不同的是，它强调阐明形式概念和证明背后的思想，以便读者快速掌握本质。
This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.