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Elliptic partial differential equations and quasiconformal mappings in the plane / Kari Astala, Tadeusz Iwaniec, and Gaven Martin.

By: Astala, Kari, 1953-.
Contributor(s): Iwaniec, Tadeusz | Martin, Gaven.
Material type: TextTextSeries: Princeton mathematical series: 48.Publisher: Princeton : Princeton University Press, c2009Description: xvi, 677 p. : USD 105.00 ill. ; 24 cm.ISBN: 9780691137773 (hardcover : acidfree paper).Subject(s): Differential equations, Elliptic | Quasiconformal mappingsDDC classification: 515.353 | 515/.93 22 Other classification: SK 560 Online resources: Table of contents only | Table of contents
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: Calderon'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.
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		515.932 AST (Browse shelf) Available 9313
Total holds: 0

Includes bibliographical references (p. 647-670) and index.

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: Calderon'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.