Boundary value problems and Hardy spaces for elliptic systems with block structure
著者
書誌事項
Boundary value problems and Hardy spaces for elliptic systems with block structure
（Progress in mathematics, v. 346）
Birkhäuser , Springer, c2023
大学図書館所蔵 件 / 全27件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"fFSB, fundació Ferran Sunyer i Balaguer"--Cover
Includes bibliographical references (p. 301-305) and index
内容説明・目次
内容説明
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 this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data.
The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions.
目次
Chapter. 1. Introduction and main resultsChapter. 2. Preliminaries on function spacesChapter. 3. Preliminaries on operator theoryChapter. 4. Hp - Hq bounded familiesChapter. 5. Conservation propertiesChapter. 6. The four critical numbersChapter. 7. Riesz transform estimates: Part IChapter. 8. Operator-adapted spacesChapter. 9. Identification of adapted Hardy spacesChapter. 10. A digression: H -calculus and analyticityChapter. 11. Riesz transform estimates: Part IIChapter. 12. Critical numbers for Poisson and heat semigroupsChapter. 13. Lp boundedness of the Hodge projectorChapter. 14. Critical numbers and kernel boundsChapter. 15. Comparison with the Auscher-Stahlhut intervalChapter. 16. Basic properties of weak solutionsChapter. 17. Existence in Hp Dirichlet and Regularity problemsChapter. 18. Existence in the Dirichlet problems with dataChapter. 19. Existence in Dirichlet problems with fractional regularity dataChapter. 20. Single layer operators for L and estimates for L-1Chapter. 21. Uniqueness in regularity and Dirichlet problemsChapter. 22. The Neumann problemAppendix A. Non-tangential maximal functions and tracesAppendix B. The Lp-realization of a sectorial operator in L2ReferencesIndex
「Nielsen BookData」 より