Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

Kari Astala is the Finnish Academy Professor of Mathematics at the University of Helsinki. Tadeusz Iwaniec is the John Raymond French Distinguished Professor of Mathematics at Syracuse University. Gaven Martin is the Distinguished Professor of Mathematics at Massey University.

"The nature of the writing is impressive, and any library owning this volume, and other volumes of he series, will be a rich library indeed. This book can work out well as a text for further study at higher graduate level and beyond. For many a mathematician, it works well as a collection of enjoyable chapters; and most importantly, it can comfortably serve well as a reference resource and study material. They will be grateful to the publishers and the authors, for the volume includes a wealth of interesting and useful information on many important topics in the subject... In short, a scintillating volume, full of detailed and thought-provoking contributions. Readers who bring to this book a reasonably strong background of the topics treated in the volume and an open mind will be well rewarded."--Current Engineering Practice

• *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: Calderon'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