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

Intro -- CONTENTS -- 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 -- The Operators K and d* -- 4. Boutet de Monvel-Type Analysis of the Boundary Value Problem -- 5. The Explicit Solution in the Case of Functions -- The a priori Estimate -- The Existence Theorem -- 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 -- The Tangential Laplacian -- The Operator GΩ on Functions -- 9. The Existence Theorem -- The Coercive Estimate -- 10. The Regularity Theorem in the Case of Functions -- The Interior Estimate -- The Boundary Estimate -- 11. Estimates for q-Forms -- The Regularity Theorem -- Proof of Theorem 11.3 -- 12. The Decomposition Theorem and Conclusions -- Proof of the Main Result -- Decomposition of W[sup(1)][sub(q)] -- 13. Final Remarks -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.