内容简介

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.

陈文雄，美国纽约Yeshiva大学终身教授，数学系主任，国际知名的数学家。曾多次获得美国国家科学基金奖。担任Nonlinear Analysis: Theory, Methods & Applications及Communications on Pure and Applied Analysis两个SCI数学杂志的编辑。研究方向为非线性偏微分方程，目前以分数阶Laplace方程为主。他曾先后在如下的SCI一区数学期刊上发表3篇论文：Annals of Mathematics: 1 篇，Communications of Pure and Applied Mathematics: 2 篇。根据Google Scholar，他在1991年Duke Math. J.上发表的名为Classification of solutions of some nonl...

目录

1: Introduction to Fractional Laplacian

2: The Green’s Function

3: Maximum Principles for the Fractional Laplacian

4: Poisson Representations

5: Liouville Type Theorems for α-Harmonic Functions

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