Contents Chapter 1. Introduction Chapter 2. Quasiconformal Mappings 2.1. Analytic Definition of Quasiconformality 2.2. The Beltrami Equation 2.3. Radial Stretchings 2.4. Classical Regularity Theory Chapter 3. Partial Differential Equations 3.1. The Transformation Formula 3.2. A Fundamental Example 3.3. The Construction 3.4. Cavitation and Riemann Surfaces Chapter 4. Mappings of Finite Distortion 4.1. Orlicz-Sobolev Spaces 4.2. Monotonicity 4.3. A Class of Orlicz Functions 4.4. The Monotonicity Theorem 4.5. Modulus of Continuity Chapter 5. Hardy Spaces and BMO 5.1. Mollifiers 5.2. Hardy-Orlicz Spaces 5.3. BMO 5.4. L log L-Integr ability 5.5. Liouville Type Theorems Chapter 6. The Principal Solution 6.1. Solutions 6.2. Uniqueness of Principal Solutions 6.3. Stoilow Factorization Chapter 7. Solutions for Integrable Distortion 7.1. Distortion in the Exponential Class 7.2. An Example 7.3. Results 7.4. Distortion in the Subexponential Class 7.5. An Example 7.6. Further Generalities 7.7. Existence Theory 1 5 5 6 7 8 11 11 12 13 15 17 18 21 22 23 24 27 27 28 29 30 30 33 33 34 35 39 41 42 43 45 45 47 48 vii
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