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Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure

In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to thi...

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Detalhes bibliográficos
Main Authors: Auscher, Pascal (Author), Egert, Moritz (Author)
Autor Corporativo: SpringerLink (Online service)
Formato: Recurso Electrónico livro electrónico
Idioma:inglês
Publicado em: Cham : Springer International Publishing : Imprint: Birkhäuser, 2023.
Edição:1st ed. 2023.
Colecção:Progress in Mathematics, 346
Assuntos:
Differential equations.
Harmonic analysis.
Operator theory.
Functional analysis.
Differential Equations.
Abstract Harmonic Analysis.
Operator Theory.
Functional Analysis.
Acesso em linha:https://doi.org/10.1007/978-3-031-29973-5
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Sumário:
  • Chapter. 1. Introduction and main results
  • Chapter. 2. Preliminaries on function spaces
  • Chapter. 3. Preliminaries on operator theory
  • Chapter. 4. Hp - Hq bounded families
  • Chapter. 5. Conservation properties
  • Chapter. 6. The four critical numbers
  • Chapter. 7. Riesz transform estimates: Part I
  • Chapter. 8. Operator-adapted spaces
  • Chapter. 9. Identification of adapted Hardy spaces
  • Chapter. 10. A digression: H -calculus and analyticity
  • Chapter. 11. Riesz transform estimates: Part II
  • Chapter. 12. Critical numbers for Poisson and heat semigroups
  • Chapter. 13. Lp boundedness of the Hodge projector
  • Chapter. 14. Critical numbers and kernel bounds
  • Chapter. 15. Comparison with the Auscher–Stahlhut interval
  • Chapter. 16. Basic properties of weak solutions
  • Chapter. 17. Existence in Hp Dirichlet and Regularity problems
  • Chapter. 18. Existence in the Dirichlet problems with data
  • Chapter. 19. Existence in Dirichlet problems with fractional regularity data
  • Chapter. 20. Single layer operators for L and estimates for L-1
  • Chapter. 21. Uniqueness in regularity and Dirichlet problems
  • Chapter. 22. The Neumann problem
  • Appendix A. Non-tangential maximal functions and traces
  • Appendix B. The Lp-realization of a sectorial operator in L2
  • References
  • Index.

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