CONTENTS
PRELIMINARIES 1
0. Introductory Remarks 1
1. Basic Notation and Definitions 3
2. Formulation of the Problem and Statement of the Main
Results 5
THE PROBLEM ON THE HALF SPACE 8
3. The Operator d* on 1-Forms and Its Domain 8
The Operators K and d* 11
4. Boutet de Monvel-Type Analysis of the Boundary Value
Problem 17
5. The Explicit Solution in the Case of Functions 23
The a priori Estimate 28
The Existence Theorem 31
6. Analysis of the Problem on the Half Space for q-Forms 37
THE CASE OF SMOOTHLY BOUNDED DOMAINS 52
7. Formulation of the Problem on a Smoothly Bounded Domain 52
8. A Special Coordinate System 59
The Tangential Laplacian 62
The Operator GQ on Functions 62
9. The Existence Theorem 64
The Coercive Estimate 67
10. The Regularity Theorem in the Case of Functions 74
The Interior Estimate 75
The Boundary Estimate 76
11. Estimates for q-Forms 79
The Regularity Theorem 79
Proof of Theorem 11.3 82
12. The Decomposition Theorem and Conclusions 89
Proof of the Main Result 89
Decomposition of W* 90
13. Final Remarks 98
References 98
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