03575nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072002300203072001600226100008800242245011200330250001800442264007900460300005200539336002600591337002600617338003600643347002400679490005900703505083200762520092201594650002802516650002502544650002102569650004002590650002802630650002502658650002102683650002702704710003402731773002602765776003602791776003602827776003602863830006602899856004602965912001403011912001503025999001703040978-3-031-63768-1DE-He21320251030112946.0cr nn 008mamaa240910s2024    sz |    s    |||| 0|eng d  a97830316376819978-3-031-63768-17 a10.1007/978-3-031-63768-12doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh 7aPBKJ2thema1 aBechtel, Sebastian.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98396310aSquare Roots of Elliptic Systems in Locally Uniform Domainsh[electronic resource] /cby Sebastian Bechtel.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2024.  aIX, 188 p. 2 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLinear Operators and Linear Systems,x2504-3617 ;v3030 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.  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 Lᵖ bounds in natural intervals of integrability parameters. This book will be useful to researchers in harmonic analysis, functional analysis and related areas. 0aDifferential equations. 0aFunctional analysis. 0aOperator theory. 0aFunctions of real variables.98396414aDifferential Equations.24aFunctional Analysis.24aOperator Theory.24aReal Functions.9839652 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303163767408iPrinted edition:z978303163769808iPrinted edition:z9783031637704 0aLinear Operators and Linear Systems,x2504-3617 ;v30398396640uhttps://doi.org/10.1007/978-3-031-63768-1  aZDB-2-SMA  aZDB-2-SXMS  c63219d63219