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020 _a9783031637681
_9978-3-031-63768-1
024 7 _a10.1007/978-3-031-63768-1
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
100 1 _aBechtel, Sebastian.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_983963
245 1 0 _aSquare Roots of Elliptic Systems in Locally Uniform Domains
_h[electronic resource] /
_cby Sebastian Bechtel.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2024.
300 _aIX, 188 p. 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLinear Operators and Linear Systems,
_x2504-3617 ;
_v303
505 0 _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.
520 _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.
650 0 _aDifferential equations.
650 0 _aFunctional analysis.
650 0 _aOperator theory.
650 0 _aFunctions of real variables.
_983964
650 1 4 _aDifferential Equations.
650 2 4 _aFunctional Analysis.
650 2 4 _aOperator Theory.
650 2 4 _aReal Functions.
_983965
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031637674
776 0 8 _iPrinted edition:
_z9783031637698
776 0 8 _iPrinted edition:
_z9783031637704
830 0 _aLinear Operators and Linear Systems,
_x2504-3617 ;
_v303
_983966
856 4 0 _uhttps://doi.org/10.1007/978-3-031-63768-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c63219
_d63219