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Elliptic partial differential equations and quasiconformal mappings in the plane [[electronic resource] /] / Kari Astala, Tadeusz Iwaniec, and Gaven Martin



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Autore: Astala Kari <1953-> Visualizza persona
Titolo: Elliptic partial differential equations and quasiconformal mappings in the plane [[electronic resource] /] / Kari Astala, Tadeusz Iwaniec, and Gaven Martin Visualizza cluster
Pubblicazione: Princeton, : Princeton University Press, c2009
Edizione: Course Book
Descrizione fisica: 1 online resource (696 p.)
Disciplina: 515/.93
Soggetto topico: Differential equations, Elliptic
Quasiconformal mappings
Soggetto non controllato: Adjoint equation
Analytic function
Analytic proof
Banach space
Beltrami equation
Boundary value problem
Bounded mean oscillation
Calculus of variations
Cantor function
Cartesian product
Cauchy–Riemann equations
Central limit theorem
Characterization (mathematics)
Complex analysis
Complex plane
Conformal geometry
Conformal map
Conjugate variables
Continuous function (set theory)
Coordinate space
Degeneracy (mathematics)
Differential equation
Directional derivative
Dirichlet integral
Dirichlet problem
Disk (mathematics)
Distribution (mathematics)
Elliptic operator
Elliptic partial differential equation
Equation
Equations of motion
Euler–Lagrange equation
Explicit formulae (L-function)
Factorization
Fourier transform
Fubini's theorem
Geometric function theory
Geometric measure theory
Geometry
Harmonic conjugate
Harmonic function
Harmonic map
Harmonic measure
Hilbert transform
Holomorphic function
Homeomorphism
Hyperbolic geometry
Hyperbolic trigonometry
Invertible matrix
Jacobian matrix and determinant
Julia set
Lagrangian (field theory)
Laplace's equation
Limit (mathematics)
Linear differential equation
Linear equation
Linear fractional transformation
Linear map
Linearization
Lipschitz continuity
Locally integrable function
Lusin's theorem
Mathematical optimization
Mathematics
Maxima and minima
Maxwell's equations
Measure (mathematics)
Metric space
Mirror symmetry (string theory)
Moduli space
Modulus of continuity
Monodromy theorem
Monotonic function
Montel's theorem
Operator (physics)
Operator theory
Partial derivative
Partial differential equation
Poisson formula
Polynomial
Quadratic function
Quasiconformal mapping
Quasiconvex function
Quasisymmetric function
Renormalization
Riemann sphere
Riemann surface
Riemannian geometry
Riesz transform
Riesz–Thorin theorem
Sign (mathematics)
Sobolev space
Square-integrable function
Support (mathematics)
Theorem
Two-dimensional space
Uniformization theorem
Upper half-plane
Variable (mathematics)
Weyl's lemma (Laplace equation)
Classificazione: SK 560
Altri autori: IwaniecTadeusz  
MartinGaven  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (p. 647-670) and index.
Nota di contenuto: Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. A Background In Conformal Geometry -- Chapter 3. The Foundations Of Quasiconformal Mappings -- Chapter 4. Complex Potentials -- Chapter 5. The Measurable Riemann Mapping Theorem: The Existence Theory Of Quasiconformal Mappings -- Chapter 6. Parameterizing General Linear Elliptic Systems -- Chapter 7. The Concept Of Ellipticity -- Chapter 8. Solving General Nonlinear First-Order Elliptic Systems -- Chapter 9. Nonlinear Riemann Mapping Theorems -- Chapter 10. Conformal Deformations And Beltrami Systems -- Chapter 11. A Quasilinear Cauchy Problem -- Chapter 12. Holomorphic Motions -- Chapter 13. Higher Integrability -- Chapter 14. Lp-Theory Of Beltrami Operators -- Chapter 15. Schauder Estimates For Beltrami Operators -- Chapter 16. Applications To Partial Differential Equations -- Chapter 17. PDEs Not Of Divergence Type: Pucci'S Conjecture -- Chapter 18. Quasiconformal Methods In Impedance Tomography: Calderón's Problem -- Chapter 19. Integral Estimates For The Jacobian -- Chapter 20. Solving The Beltrami Equation: Degenerate Elliptic Case -- Chapter 21. Aspects Of The Calculus Of Variations -- Appendix: Elements Of Sobolev Theory And Function Spaces -- Basic Notation -- Bibliography -- Index
Sommario/riassunto: 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 compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Titolo autorizzato: Elliptic partial differential equations and quasiconformal mappings in the plane  Visualizza cluster
ISBN: 1-282-15727-2
9786612157271
1-4008-3011-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910778138403321
Lo trovi qui: Univ. Federico II
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Serie: Princeton mathematical series ; ; 48.