Geometric Harmonic Analysis V: Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems

Mitrea, Dorina, Mitrea, Irina, Mitrea, Marius

  • 出版商: Springer
  • 出版日期: 2024-08-24
  • 售價: $7,630
  • 貴賓價: 9.5$7,249
  • 語言: 英文
  • 頁數: 994
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031315634
  • ISBN-13: 9783031315633
  • 海外代購書籍(需單獨結帳)

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商品描述

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.

The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.


商品描述(中文翻譯)

本專著透過五個漸進的卷數,提出了一種全面、自足且新穎的散度定理方法。其最終目的是發展具幾何測度理論風格的實分析和調和分析工具,能夠處理在相當一般的幾何和分析背景下所形成的廣泛邊界值問題。該文本旨在為研究人員、研究生及對調和分析和幾何測度理論在複分析、散射及偏微分方程應用感興趣的業界專業人士提供參考。

第五卷的最終目標是證明關於橢圓二階齊次常數(複數)係數系統的邊界值問題的良好適定性和Fredholm可解性結果,以及相當一般幾何性質的區域。這裡所處理的邊界值問題的表述從多個角度來看都是最佳的,涉及幾何、泛函分析(通過考慮各種函數空間的尺度)、拓撲學和偏微分方程。