| eBook ISBN: | 978-1-4704-0211-2 |
| Product Code: | MEMO/131/622.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
| eBook ISBN: | 978-1-4704-0211-2 |
| Product Code: | MEMO/131/622.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 131; 1998; 100 ppMSC: Primary 35; 58
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
ReadershipGraduate students, research mathematicians, control theorists, engineers and physicists working in boundary value problems for elliptic systems.
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Table of Contents
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Chapters
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Preliminaries
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0. Introductory remarks
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1. Basic notation and definitions
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2. Formulation of the problem and statement of the main results
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The problem on the half space
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3. The operator $d$* on 1-forms and its domain
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4. Boutet De Monvel-type analysis of the boundary value problem
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5. The explicit solution in the case of functions
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6. Analysis of the problem on the half space for $q$-forms
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The case of smoothly bounded domains
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7. Formulation of the problem on a smoothly bounded domain
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8. A special coordinate system
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9. The existence theorem
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10. The regularity theorem in the case of functions
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11. Estimates for $q$-forms
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12. The decomposition theorem and conclusions
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13. Final remarks
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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
Graduate students, research mathematicians, control theorists, engineers and physicists working in boundary value problems for elliptic systems.
-
Chapters
-
Preliminaries
-
0. Introductory remarks
-
1. Basic notation and definitions
-
2. Formulation of the problem and statement of the main results
-
The problem on the half space
-
3. The operator $d$* on 1-forms and its domain
-
4. Boutet De Monvel-type analysis of the boundary value problem
-
5. The explicit solution in the case of functions
-
6. Analysis of the problem on the half space for $q$-forms
-
The case of smoothly bounded domains
-
7. Formulation of the problem on a smoothly bounded domain
-
8. A special coordinate system
-
9. The existence theorem
-
10. The regularity theorem in the case of functions
-
11. Estimates for $q$-forms
-
12. The decomposition theorem and conclusions
-
13. Final remarks
