Elliptic partial differential equations and quasiconformal mappings in the plane /
This 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 compellin...
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| Main Author: | |
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ :
Princeton University Press,
2009
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| Series: | Princeton mathematical series ;
48. |
| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- Background in conformal geometry
- Foundations of quasiconformal mappings
- Complex potentials
- Measurable Riemann mapping theorem: the existence theory of quasiconformal mappings
- Parameterizing general linear elliptic systems
- Concept of ellipticity
- Solving general nonlinear first-order elliptic systems
- Nonlinear Riemann mapping theorems
- Conformal deformations and beltrami systems
- Quasilinear cauchy problem
- Holomorphic motions
- Higher Integrability
- L[superscript 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 spaces
- A.1. Schwartz distributions
- A.2. Definitions of Sobolev spaces
- A.3. Mollification
- A.4. Pointwise coincidence of Sobolev functions
- A.5. Alternate characterizations
- A.6. Embedding theorems
- A.7. Duals and compact embeddings
- A.8. Hardy spaces and BMO
- A.9. Reverse holder inequalities
- A.10. Variations of Sobolev mappings.
