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The Fractional Laplacian
Wenxiong ChenYan LiPei Ma
出版World Scientific, 2020-06-09
主題Mathematics / Mathematical AnalysisMathematics / Functional AnalysisMathematics / Differential Equations / PartialMathematics / Calculus
ISBN98132240109789813224018
URLhttp://books.google.com.hk/books?id=mdrrDwAAQBAJ&hl=&source=gbs_api
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註釋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.