索伯列夫空间
2009-8
世界图书出版公司
亚当斯
305
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This monograph presents an introductory study of of the properties of certain Ba-nach spaces of weakly differentiable functions of several real variables that arise inconnection with numerous problems in the theory of partial differential equations，approximation theory， and many other areas of pure and applied mathematics.These spaces have become associated with the name of the late Russian mathe-matician S. L. Sobolev， although their origins predate his major contributions totheir development in the late 1930s. Even by 1975 when the first edition of this monograph was published， there wasa great deal of material on these spaces and their close relatives， though most of itwas available only in research papers published in a wide variety of journals. Themonograph was written to fill a perceived need for a single source where graduatestudents and researchers in a wide variety of disciplines could learn the essentialfeatures of Sobolev spaces that they needed for their particular applications. Noattempt was made even at that time for complete coverage. To quote from thePreface of the first edition.
This monograph presents an introductory study of of the properties of certain Ba-nach spaces of weakly differentiable functions of several real variables that arise inconnection with numerous problems in the theory of partial differential equations，approximation theory，and many other areas of pure and applied mathematics.These spaces have become associated with the name of the late Russian mathe-matician S. L. Sobolev，although their origins predate his major contributions totheir development in the late 1930s.
Preface Lisf of Spaces and Norms1. PRELIMINARIES Notation Topological Vector Spaces Normed Spaces Spaces of Continuous Functions The Lebesgue Measure in Rn The Lebesgue Integral Distributions and Weak Derivatives2. THE LEBESGUE SPACES Lp(Ω) Definition and Basic Properties Completeness of Lp (Ω) Approximation by Continuous Functions Convolutions and Young's Theorem Mollifiers and Approximation by Smooth Functions Precompact Sets in Lp (Ω) Uniform Convexity The Normed Dual of LP(Ω) Mixed-Norm Lp Spaces The Marcinkiewicz Interpolation Theorem……
The existing mathematical literature on Sobolev spaces and theirgeneralizations is vast， and it would be neither easy nor particularlydesirable to include everything that was known about such spacesbetween the covers of one book. An attempt has been made in thismonograph to present all the core material in sufficient generality tocover most applications， to give the reader an overview of the subjectthat is difficult to obtain by reading research papers， and finally ...to provide a ready reference for someone requiring a result aboutSobolev spaces for use in some application.
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Adams这本索伯列夫空间是有关索伯列夫空间理论的经典之作，是研究偏微分方程的科研人员必读的经典。
此书是sobolev空间方面的经典教材，也是我们的教学用书
对于学习现代偏微分方程理论是必要的