Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

FrontMatter, pg. i
Contents, pg. vii
Preface, pg. xv
Chapter 1. Introduction, pg. 1
Chapter 2. A Background In Conformal Geometry, pg. 12
Chapter 3. The Foundations Of Quasiconformal Mappings, pg. 48
Chapter 4. Complex Potentials, pg. 92
Chapter 5. The Measurable Riemann Mapping Theorem: The Existence Theory Of Quasiconformal Mappings, pg. 161
Chapter 6. Parameterizing General Linear Elliptic Systems, pg. 195
Chapter 7. The Concept Of Ellipticity, pg. 210
Chapter 8. Solving General Nonlinear First-Order Elliptic Systems, pg. 235
Chapter 9. Nonlinear Riemann Mapping Theorems, pg. 259
Chapter 10. Conformal Deformations And Beltrami Systems, pg. 275
Chapter 11. A Quasilinear Cauchy Problem, pg. 289
Chapter 12. Holomorphic Motions, pg. 293
Chapter 13. Higher Integrability, pg. 316
Chapter 14. Lp-Theory Of Beltrami Operators, pg. 362
Chapter 15. Schauder Estimates For Beltrami Operators, pg. 389
Chapter 16. Applications To Partial Differential Equations, pg. 403
Chapter 17. PDEs Not Of Divergence Type: Pucci'S Conjecture, pg. 472
Chapter 18. Quasiconformal Methods In Impedance Tomography: Calderón's Problem, pg. 490
Chapter 19. Integral Estimates For The Jacobian, pg. 514
Chapter 20. Solving The Beltrami Equation: Degenerate Elliptic Case, pg. 527
Chapter 21. Aspects Of The Calculus Of Variations, pg. 586
Appendix: Elements Of Sobolev Theory And Function Spaces, pg. 624
Basic Notation, pg. 643
Bibliography, pg. 647
Index, pg. 671