LEADER 05569nam 22014655 450 001 9910154743903321 005 20190708092533.0 010 $a1-4008-8152-8 024 7 $a10.1515/9781400881529 035 $a(CKB)3710000000631368 035 $a(SSID)ssj0001651302 035 $a(PQKBManifestationID)16425718 035 $a(PQKBTitleCode)TC0001651302 035 $a(PQKBWorkID)12671753 035 $a(PQKB)10084430 035 $a(MiAaPQ)EBC4738518 035 $a(DE-B1597)468040 035 $a(OCoLC)979970555 035 $a(DE-B1597)9781400881529 035 $a(EXLCZ)993710000000631368 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Neumann Problem for the Cauchy-Riemann Complex. (AM-75), Volume 75 /$fJoseph John Kohn, Gerald B. Folland 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1973 215 $a1 online resource (157 pages) 225 0 $aAnnals of Mathematics Studies ;$v234 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08120-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tFOREWORD -- $tTABLE OF CONTENTS -- $tCHAPTER I. FORMULATION OF THE PROBLEM -- $tCHAPTER II. THE MAIN THEOREM -- $tCHAPTER III. INTERPRETATION OF THE MAIN THEOREM -- $tCHAPTER IV. APPLICATIONS -- $tCHAPTER V. THE BOUNDARY COMPLEX -- $tCHAPTER VI. OTHER METHODS AND RESULTS -- $tAPPENDIX: THE FUNCTIONAL ANALYSIS OF DIFFERENTIAL OPERATORS -- $tREFERENCES -- $tTERMINOLOGICAL INDEX -- $tTERMINOLOGICAL INDEX 330 $aPart explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph. 410 0$aAnnals of mathematics studies ;$vNumber 75. 606 $aNeumann problem 606 $aDifferential operators 606 $aComplex manifolds 610 $aA priori estimate. 610 $aAlmost complex manifold. 610 $aAnalytic function. 610 $aApply. 610 $aApproximation. 610 $aBernhard Riemann. 610 $aBoundary value problem. 610 $aCalculation. 610 $aCauchy?Riemann equations. 610 $aCohomology. 610 $aCompact space. 610 $aComplex analysis. 610 $aComplex manifold. 610 $aCoordinate system. 610 $aCorollary. 610 $aDerivative. 610 $aDifferentiable manifold. 610 $aDifferential equation. 610 $aDifferential form. 610 $aDifferential operator. 610 $aDimension (vector space). 610 $aDirichlet boundary condition. 610 $aEigenvalues and eigenvectors. 610 $aElliptic operator. 610 $aEquation. 610 $aEstimation. 610 $aEuclidean space. 610 $aExistence theorem. 610 $aExterior (topology). 610 $aFinite difference. 610 $aFourier analysis. 610 $aFourier transform. 610 $aFrobenius theorem (differential topology). 610 $aFunctional analysis. 610 $aHilbert space. 610 $aHodge theory. 610 $aHolomorphic function. 610 $aHolomorphic vector bundle. 610 $aIrreducible representation. 610 $aLine segment. 610 $aLinear programming. 610 $aLocal coordinates. 610 $aLp space. 610 $aManifold. 610 $aMonograph. 610 $aMulti-index notation. 610 $aNonlinear system. 610 $aOperator (physics). 610 $aOverdetermined system. 610 $aPartial differential equation. 610 $aPartition of unity. 610 $aPotential theory. 610 $aPower series. 610 $aPseudo-differential operator. 610 $aPseudoconvexity. 610 $aPseudogroup. 610 $aPullback. 610 $aRegularity theorem. 610 $aRemainder. 610 $aScientific notation. 610 $aSeveral complex variables. 610 $aSheaf (mathematics). 610 $aSmoothness. 610 $aSobolev space. 610 $aSpecial case. 610 $aStatistical significance. 610 $aSturm?Liouville theory. 610 $aSubmanifold. 610 $aTangent bundle. 610 $aTheorem. 610 $aUniform norm. 610 $aVector field. 610 $aWeight function. 615 0$aNeumann problem. 615 0$aDifferential operators. 615 0$aComplex manifolds. 676 $a515/.353 700 $aFolland$b Gerald B., $041512 702 $aKohn$b Joseph John, 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154743903321 996 $aThe Neumann Problem for the Cauchy-Riemann Complex. 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