A Course in the Calculus of Variations : Optimization, Regularity, and Modeling (Universitext)

個数:

A Course in the Calculus of Variations : Optimization, Regularity, and Modeling (Universitext)

  • 提携先の海外書籍取次会社に在庫がございます。通常3週間で発送いたします。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合は、ご注文数量が揃ってからまとめて発送いたします。
    3. 美品のご指定は承りかねます。

    ●3Dセキュア導入とクレジットカードによるお支払いについて
  • 【入荷遅延について】
    世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
    おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。
  • ◆画像の表紙や帯等は実物とは異なる場合があります。
  • ◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
    また、洋書販売価格は、ご注文確定時点での日本円価格となります。
    ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。
  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 338 p.
  • 商品コード 9783031450358

Full Description

This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.
Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality andthe Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence.
While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

Contents

1 One-dimensional variational problems.- 2 Multi-dimensional variational problems.- 3  Lower semicontinuity.- 4  Convexity and its applications.- 5 Hölder regularity.- 6 Variational problems for sets.- 7 Γ-convergence: theory and examples.

最近チェックした商品