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[ 洋図書 ] Isolated singularities in partial differential inequalities / ( Encyclopedia of mathematics and its applications ; no. 161 )

Marius Ghergu, Steven D. Taliaferro. -- Cambridge University Press, -- 2016. --

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ISBN 1107138388
ISBN13桁 9781107138384
テキストの言語 英語                  
分類：NDC10版 410.8
個人著者標目 Ghergu, Marius,
本タイトル Isolated singularities in partial differential inequalities /
著者名 Marius Ghergu, Steven D. Taliaferro.
出版地・頒布地 Cambridge :
出版者・頒布者名 Cambridge University Press,
出版年・頒布年 2016.
数量 xii, 349 pages ;
大きさ 25 cm
書誌注記 Includes bibliographical references (pages 341-347) and index.
内容注記 Representation formulae for singular solutions of polyharmonic and parabolic inequalities -- Isolated singularities of nonlinear second-order elliptic inequalities -- More on isolated singularities for semilinear elliptic inequalities -- Elliptic inequalities for the Laplace operator with Hardy potential -- Singular solutions for second-order nondivergence type elliptic inequalities -- Isolated singularities of polyharmonic inequalities -- Isolated singularities of polyharmonic inequalities -- Nonlinear biharmonic inequalities -- Semilinear elliptic systems of differential inequalities -- Isolated singularities for nonlocal elliptic systems -- Isolated singularities for systems of parabolic inequalities -- Appendixes: A. Estimates for the heat kernel -- B. Heat potential estimates -- C. Nonlinear potential estimates.
要約、抄録、注釈等 In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.
著者標目 Taliaferro, Steven D.,
統一タイトル(シリーズ副出標目) Encyclopedia of mathematics and its applications ;
シリーズの巻次 no. 161.
シリーズ名・巻次 Encyclopedia of mathematics and its applications ; no. 161
一般件名 Inequalities (Mathematics)
Singularities (Mathematics)
資料情報1 『Isolated singularities in partial differential inequalities /』（Encyclopedia of mathematics and its applications ; no. 161）　Marius Ghergu, Steven D. Taliaferro.　Cambridge University Press,　2016. （所蔵館：中央　 請求記号：F/410.8/E56/E1-161　 資料コード：7107755720）
URL https://catalog.library.metro.tokyo.lg.jp/winj/opac/switch-detail.do?lang=ja&bibid=1352020325

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