LEADER 08590nam 2201897 a 450 001 9910778138403321 005 20200520144314.0 010 $a1-282-15727-2 010 $a9786612157271 010 $a1-4008-3011-7 024 7 $a10.1515/9781400830114 035 $a(CKB)1000000000788392 035 $a(EBL)457704 035 $a(OCoLC)441714631 035 $a(SSID)ssj0000145540 035 $a(PQKBManifestationID)11158175 035 $a(PQKBTitleCode)TC0000145540 035 $a(PQKBWorkID)10157187 035 $a(PQKB)11536684 035 $a(DE-B1597)446543 035 $a(OCoLC)979629198 035 $a(DE-B1597)9781400830114 035 $a(Au-PeEL)EBL457704 035 $a(CaPaEBR)ebr10312571 035 $a(CaONFJC)MIL215727 035 $a(MiAaPQ)EBC457704 035 $a(PPN)170267253 035 $a(EXLCZ)991000000000788392 100 $a20080821d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic partial differential equations and quasiconformal mappings in the plane$b[electronic resource] /$fKari Astala, Tadeusz Iwaniec, and Gaven Martin 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$dc2009 215 $a1 online resource (696 p.) 225 1 $aPrinceton mathematical series ;$v48 300 $aDescription based upon print version of record. 311 $a0-691-13777-3 320 $aIncludes bibliographical references (p. 647-670) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter 1. Introduction -- $tChapter 2. A Background In Conformal Geometry -- $tChapter 3. The Foundations Of Quasiconformal Mappings -- $tChapter 4. Complex Potentials -- $tChapter 5. The Measurable Riemann Mapping Theorem: The Existence Theory Of Quasiconformal Mappings -- $tChapter 6. Parameterizing General Linear Elliptic Systems -- $tChapter 7. The Concept Of Ellipticity -- $tChapter 8. Solving General Nonlinear First-Order Elliptic Systems -- $tChapter 9. Nonlinear Riemann Mapping Theorems -- $tChapter 10. Conformal Deformations And Beltrami Systems -- $tChapter 11. A Quasilinear Cauchy Problem -- $tChapter 12. Holomorphic Motions -- $tChapter 13. Higher Integrability -- $tChapter 14. Lp-Theory Of Beltrami Operators -- $tChapter 15. Schauder Estimates For Beltrami Operators -- $tChapter 16. Applications To Partial Differential Equations -- $tChapter 17. PDEs Not Of Divergence Type: Pucci'S Conjecture -- $tChapter 18. Quasiconformal Methods In Impedance Tomography: Calderón's Problem -- $tChapter 19. Integral Estimates For The Jacobian -- $tChapter 20. Solving The Beltrami Equation: Degenerate Elliptic Case -- $tChapter 21. Aspects Of The Calculus Of Variations -- $tAppendix: Elements Of Sobolev Theory And Function Spaces -- $tBasic Notation -- $tBibliography -- $tIndex 330 $aThis book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings. 410 0$aPrinceton mathematical series ;$v48. 606 $aDifferential equations, Elliptic 606 $aQuasiconformal mappings 610 $aAdjoint equation. 610 $aAnalytic function. 610 $aAnalytic proof. 610 $aBanach space. 610 $aBeltrami equation. 610 $aBoundary value problem. 610 $aBounded mean oscillation. 610 $aCalculus of variations. 610 $aCantor function. 610 $aCartesian product. 610 $aCauchy?Riemann equations. 610 $aCentral limit theorem. 610 $aCharacterization (mathematics). 610 $aComplex analysis. 610 $aComplex plane. 610 $aConformal geometry. 610 $aConformal map. 610 $aConjugate variables. 610 $aContinuous function (set theory). 610 $aCoordinate space. 610 $aDegeneracy (mathematics). 610 $aDifferential equation. 610 $aDirectional derivative. 610 $aDirichlet integral. 610 $aDirichlet problem. 610 $aDisk (mathematics). 610 $aDistribution (mathematics). 610 $aElliptic operator. 610 $aElliptic partial differential equation. 610 $aEquation. 610 $aEquations of motion. 610 $aEuler?Lagrange equation. 610 $aExplicit formulae (L-function). 610 $aFactorization. 610 $aFourier transform. 610 $aFubini's theorem. 610 $aGeometric function theory. 610 $aGeometric measure theory. 610 $aGeometry. 610 $aHarmonic conjugate. 610 $aHarmonic function. 610 $aHarmonic map. 610 $aHarmonic measure. 610 $aHilbert transform. 610 $aHolomorphic function. 610 $aHomeomorphism. 610 $aHyperbolic geometry. 610 $aHyperbolic trigonometry. 610 $aInvertible matrix. 610 $aJacobian matrix and determinant. 610 $aJulia set. 610 $aLagrangian (field theory). 610 $aLaplace's equation. 610 $aLimit (mathematics). 610 $aLinear differential equation. 610 $aLinear equation. 610 $aLinear fractional transformation. 610 $aLinear map. 610 $aLinearization. 610 $aLipschitz continuity. 610 $aLocally integrable function. 610 $aLusin's theorem. 610 $aMathematical optimization. 610 $aMathematics. 610 $aMaxima and minima. 610 $aMaxwell's equations. 610 $aMeasure (mathematics). 610 $aMetric space. 610 $aMirror symmetry (string theory). 610 $aModuli space. 610 $aModulus of continuity. 610 $aMonodromy theorem. 610 $aMonotonic function. 610 $aMontel's theorem. 610 $aOperator (physics). 610 $aOperator theory. 610 $aPartial derivative. 610 $aPartial differential equation. 610 $aPoisson formula. 610 $aPolynomial. 610 $aQuadratic function. 610 $aQuasiconformal mapping. 610 $aQuasiconvex function. 610 $aQuasisymmetric function. 610 $aRenormalization. 610 $aRiemann sphere. 610 $aRiemann surface. 610 $aRiemannian geometry. 610 $aRiesz transform. 610 $aRiesz?Thorin theorem. 610 $aSign (mathematics). 610 $aSobolev space. 610 $aSquare-integrable function. 610 $aSupport (mathematics). 610 $aTheorem. 610 $aTwo-dimensional space. 610 $aUniformization theorem. 610 $aUpper half-plane. 610 $aVariable (mathematics). 610 $aWeyl's lemma (Laplace equation). 615 0$aDifferential equations, Elliptic. 615 0$aQuasiconformal mappings. 676 $a515/.93 686 $aSK 560$2rvk 700 $aAstala$b Kari$f1953-$0471671 701 $aIwaniec$b Tadeusz$066901 701 $aMartin$b Gaven$044012 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778138403321 996 $aElliptic partial differential equations and quasiconformal mappings in the plane$9803363 997 $aUNINA