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010   $a3-031-63768-2
024 7 $a10.1007/978-3-031-63768-1
035   $a(MiAaPQ)EBC31654310
035   $a(Au-PeEL)EBL31654310
035   $a(CKB)34975738800041
035   $a(DE-He213)978-3-031-63768-1
035   $a(EXLCZ)9934975738800041
100   $a20240910d2024      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aSquare Roots of Elliptic Systems in Locally Uniform Domains /$fby Sebastian Bechtel
205   $a1st ed. 2024.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2024.
215   $a1 online resource (191 pages)
225 1 $aLinear Operators and Linear Systems,$x2504-3617 ;$v303
311 08$a3-031-63767-4 
327   $aIntroduction -- Locally uniform domains -- A density result for locally uniform domains -- Sobolev extension operator -- A short account on sectorial and bisectorial operators -- Elliptic systems in divergence form -- Porous sets -- Sobolev spaces with a vanishing trace condition -- Hardy?s inequality -- Real interpolation of Sobolev spaces -- Higher regularity for fractional powers of the Laplacian -- First order formalism -- Kato?s square root property on thick sets -- Removing the thickness condition -- Interlude: Extension operators for fractional Sobolev spaces -- Critical numbers and Lp ? Lq bounded families of operators -- Lp-bounds for the H1-calculus and Riesz transform -- Calder´on?Zygmund decomposition for Sobolev functions -- Lp bounds for square roots of elliptic systems -- References -- Index.
330   $aThis book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions. To lay the groundwork, the text begins by introducing the geometry of locally uniform domains and establishes theory for function spaces on locally uniform domains, including interpolation theory and extension operators. In these introductory parts, fundamental knowledge on function spaces, interpolation theory and geometric measure theory and fractional dimensions are recalled, making the main content of the book easier to comprehend. The centerpiece of the book is the solution to Kato's square root problem on locally uniform domains. The Kato result is complemented by corresponding L? bounds in natural intervals of integrability parameters. This book will be useful to researchers in harmonic analysis, functional analysis and related areas.
410  0$aLinear Operators and Linear Systems,$x2504-3617 ;$v303
606   $aDifferential equations
606   $aFunctional analysis
606   $aOperator theory
606   $aFunctions of real variables
606   $aDifferential Equations
606   $aFunctional Analysis
606   $aOperator Theory
606   $aReal Functions
615  0$aDifferential equations.
615  0$aFunctional analysis.
615  0$aOperator theory.
615  0$aFunctions of real variables.
615 14$aDifferential Equations.
615 24$aFunctional Analysis.
615 24$aOperator Theory.
615 24$aReal Functions.
676   $a515.35
700   $aBechtel$b Sebastian$01768512
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910886993203321
996   $aSquare Roots of Elliptic Systems in Locally Uniform Domains$94229476
997   $aUNINA