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Hodge Theory in the Sobolev Topology for the de Rham Complex
Luigi Fontana, Universita di Milano, Italy, Steven G. Krantz, Washington University, St. Louis, MO, and Marco M. Peloso, Politecnico di Torino, Italy
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Memoirs of the American Mathematical Society
1998; 100 pp; softcover
Volume: 131
ISBN-10: 0-8218-0830-3
ISBN-13: 978-0-8218-0830-6
List Price: US$45
Individual Members: US$27
Institutional Members: US$36
Order Code: MEMO/131/622
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In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the \(L^2\) topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain.

Features:

  • a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems
  • theorems completely explained and proved
  • new geometric tools for differential analysis on domains and manifolds

Readership

Graduate students, research mathematicians, control theorists, engineers and physicists working in boundary value problems for elliptic systems.

Table of Contents

  • Preliminaries
  • The problem on the half space
  • The case of smoothly bounded domains
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