**Memoirs of the American Mathematical Society**

1998;
100 pp;
Softcover

MSC: Primary 35; 58;

Print ISBN: 978-0-8218-0830-6

Product Code: MEMO/131/622

List Price: $48.00

Individual Member Price: $28.80

**Electronic ISBN: 978-1-4704-0211-2
Product Code: MEMO/131/622.E**

List Price: $48.00

Individual Member Price: $28.80

# Hodge Theory in the Sobolev Topology for the de Rham Complex

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*Luigi Fontana; Steven G. Krantz; Marco M. Peloso*

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

#### Table of Contents

# Table of Contents

## Hodge Theory in the Sobolev Topology for the de Rham Complex

- CONTENTS vii8 free
- PRELIMINARIES 110 free
- THE PROBLEM ON THE HALF SPACE 817
- THE CASE OF SMOOTHLY BOUNDED DOMAINS 5261

#### Readership

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