Unbounded functionals in the calculus of variations ; representation, relaxation, and homogenization
著者
書誌事項
Unbounded functionals in the calculus of variations ; representation, relaxation, and homogenization
(Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 125)
Chapman & Hall/CRC, c2002
大学図書館所蔵 全21件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
T.p. verso inserted.
内容説明・目次
内容説明
Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a general theory of integral representation, relaxation, and homogenization for unbounded functionals.
The first part of the book builds the foundation for the general theory with concepts and tools from convex analysis, measure theory, and the theory of variational convergences. The authors then introduce some function spaces and explore some lower semicontinuity and minimization problems for energy functionals. Next, they survey some specific aspects the theory of standard functionals.
The second half of the book carefully develops a theory of unbounded, translation invariant functionals that leads to results deeper than those already known, including unique extension properties, representation as integrals of the calculus of variations, relaxation theory, and homogenization processes. In this study, some new phenomena are pointed out. The authors' approach is unified and elegant, the text well written, and the results intriguing and useful, not just in various fields of mathematics, but also in a range of applied mathematics, physics, and material science disciplines.
目次
Preface. Basic Notations and Recalls. Elements of Convex Analysis. Elements of Measure and Increasing Set Functions . Minimization Methods and Variational Convergences. Bv and Sobolev Spaces. Lower Semicontinuity and Minimization of Integral Functionals. Classical Results and Mathematical Models . Abstract Regularization and Jensen's Inequality. Unique Extension Results. Integral Representation for Unbounded Functionals. Relaxation of Unbounded Functionals. Cut-off Functions and Partitions of Unity. Homogenization of Unbounded Functionals. Homogenization of Unbounded Functionals with Special Constraints Set. Bibliography. Index.
「Nielsen BookData」 より