02279nam a2200337 i 4500991000331679707536090714s2009 njua b 001 0 eng d97806911377730691137773b13842213-39ule_instDip.to Matematicaeng515.9322AMS 35J60LC QA377.A836Astala, Kari471671Elliptic partial differential equations and quasiconformal mappings in the plane /Kari Astala, Tadeusz Iwaniec, and Gaven MartinPrinceton ; Oxford :Princeton University Press,c2009xvi, 677 p. :ill. ;24 cmPrinceton mathematical series,0079-5194 ;48Includes bibliographical references (p. 647-670) and indexIntroduction ; A background in conformal geometry ; The foundations of quasiconformal mappings ; Complex potentials ; The measurable Riemann mapping theorem : the existence theory of quasiconformal mappings ; Parameterizing general linear elliptic systems ; The concept of ellipticity ; Solving general nonlinear first-order elliptic systems ; Nonlinear Riemann mapping theorems ; Conformal deformations and Beltrami systems ; A quasilinear Cauchy problem ; Holomorphic motions ; Higher integrability ; L[p]-theory of Beltrami operators ; Schauder estimates for Beltrami operators ; Applications to partial differential equations ; PDEs not of divergence type : Pucci's conjecture ; Quasiconformal methods in impedance tomography : Calderón's problem ; Integral estimates for the Jacobian ; Solving the Beltrami equation : Degenerate elliptic case ; Aspects of the calculus of variations ; Appendix: Elements of Sobolev theory and function spacesDifferential equations, EllipticQuasiconformal mappingsIwaniec, TadeuszMartin, Gaven.b1384221302-04-1414-07-09991000331679707536LE013 35J AST11 (2009)12013000292243le013pE57.47-l- 00000.i1500322x17-09-09Elliptic partial differential equations and quasiconformal mappings in the plane229584UNISALENTOle01314-07-09ma -engnju00