what so notis not robert bucksbaum's job

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复习课件 Unit 4 Robert is not well_百度文库
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复习课件 Unit 4 Robert is not well
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你可能喜欢What Is Not in the Domain of the Laplacian on Sierpinski Gasket Type Fractals - ScienceDirect
Download PDFDownloadExport JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page., 20 August 1999, Pages 197-217Author links open overlay panelShow moreopen archiveAbstractWe consider the analog of the Laplacian on the Sierpinski gasket and related fractals, constructed by Kigami. A function f is said to belong to the domain of Δ if f is continuous and Δf is defined as a continuous function. We show that if f is a nonconstant function in the domain of Δ, then f2 is not in the domain of Δ. We give two proofs of this fact. The first is based on the analog of the pointwise identity Δf2-2f Δf=|?f|2, where we show that |?f|2 does not exist as a continuous function. In fact the correct interpretation of Δf2 is as a singular measure, a result due to K we give a new proof of this fact. The second is based on a dichotomy for the local behavior of a function in the domain of Δ, at a junction point x0 of the fractal: in the typical case (nonvanishing of the normal derivative) we have upper and lower bounds for |f(x)-f(x0)| in terms of d(x, x0)β for a certain value β, and in the nontypical case (vanishing normal derivative) we have an upper bound with an exponent greater than 2. This method allows us to show that general nonlinear functions do not operate on the domain of Δ.Recommended articlesCiting articles (0)2016新概念第一册 Lesson 7-8 课堂及课后练习_百度文库
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2016新概念第一册 Lesson 7-8 课堂及课后练习
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