LEADER 05020nam 22007215 450 001 9910736007303321 005 20240509105206.0 010 $a3-031-29973-6 024 7 $a10.1007/978-3-031-29973-5 035 $a(MiAaPQ)EBC30668286 035 $a(Au-PeEL)EBL30668286 035 $a(DE-He213)978-3-031-29973-5 035 $a(PPN)272250694 035 $a(CKB)27867631600041 035 $a(EXLCZ)9927867631600041 100 $a20230727d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBoundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure /$fby Pascal Auscher, Moritz Egert 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (310 pages) 225 1 $aProgress in Mathematics,$x2296-505X ;$v346 311 08$aPrint version: Auscher, Pascal Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure Cham : Springer International Publishing AG,c2023 9783031299728 327 $aChapter. 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. 330 $aIn this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data. The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions. 410 0$aProgress in Mathematics,$x2296-505X ;$v346 606 $aDifferential equations 606 $aHarmonic analysis 606 $aOperator theory 606 $aFunctional analysis 606 $aDifferential Equations 606 $aAbstract Harmonic Analysis 606 $aOperator Theory 606 $aFunctional Analysis 606 $aEquacions diferencials el·líptiques$2thub 606 $aProblemes de contorn$2thub 606 $aEspais de Hardy$2thub 608 $aLlibres electrònics$2thub 615 0$aDifferential equations. 615 0$aHarmonic analysis. 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aDifferential Equations. 615 24$aAbstract Harmonic Analysis. 615 24$aOperator Theory. 615 24$aFunctional Analysis. 615 7$aEquacions diferencials el·líptiques 615 7$aProblemes de contorn 615 7$aEspais de Hardy 676 $a515.353 700 $aAuscher$b Pascal$0282068 701 $aEgert$b Moritz$01380498 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910736007303321 996 $aBoundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure$93421931 997 $aUNINA