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Hodge theory in the Sobolev topology for the de Rham complex

About this Title

Luigi Fontana, Steven G. Krantz and Marco M. Peloso

Publication: Memoirs of the American Mathematical Society
Publication Year 1998: Volume 131, Number 622
ISBNs: 978-0-8218-0830-6 (print); 978-1-4704-0211-2 (online)
MathSciNet review: 1434991
MSC: Primary 58G20; Secondary 35J25, 35N15, 35S05, 47F05, 58A14, 58G05

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Table of 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
  • 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
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