03898nam 2200589 450 991078861810332120180731043852.00-8218-9008-5(CKB)3360000000464083(EBL)3114581(SSID)ssj0000889089(PQKBManifestationID)11932397(PQKBTitleCode)TC0000889089(PQKBWorkID)10875138(PQKB)11515324(MiAaPQ)EBC3114581(RPAM)17226579(PPN)19541912X(EXLCZ)99336000000046408320150416h20122012 uy 0engur|n|---|||||txtccrn-harmonic mappings between annuli the art of integrating free Lagrangians /Tadeusz Iwaniec, Jani OnninenProvidence, Rhode Island :American Mathematical Society,2012.©20121 online resource (105 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 218, Number 1023"July 2012, Volume 218, Number 1023 (first of 5 numbers)."0-8218-5357-0 Includes bibliographical references.""Contents""; ""Preface""; ""Chapter 1. Introduction and Overview""; ""1. Basic notation""; ""2. Mathematical model of hyperelasticity""; ""3. Variational integrals in GFT""; ""4. Conformal energy""; ""5. Weak limits of homeomorphisms""; ""6. Annuli""; ""7. Hammering a part of an annulus into a circle, n=2""; ""8. Principal n-harmonics""; ""9. Elasticity of stretching""; ""10. Conformally expanding pair""; ""11. Conformally contracting pair""; ""12. The conformal case Mod A = Mod A""; ""13. The energy function Fh""; ""14. Free Lagrangians""; ""15. Uniqueness""""16. The L1-theory of inner distortion""""Conclusion""; ""Part 1. Principal Radial n-Harmonics""; ""Chapter 2. Nonexistence of n-Harmonic Homeomorphisms""; ""Chapter 3. Generalized n-Harmonic Mappings""; ""1. Solutions to the generalized n-harmonic equation that are not n-harmonic""; ""2. Slipping along the boundaries""; ""3. Proof of Theorem 1.7""; ""Chapter 4. Notation""; ""1. Annuli and their modulus""; ""2. Polar coordinates in Rn""; ""3. Spherical coordinates, latitude and longitude""; ""4. Radial stretching""; ""5. Spherical mappings""; ""Chapter 5. Radial n-Harmonics""""1. The n-Laplacian for the strain function""""2. The principal solutions""; ""3. The elasticity function""; ""4. The principal solution H+ (conformal contraction)""; ""5. The principal solution H- (conformal expansion)""; ""6. The boundary value problem for radial n-harmonics""; ""Chapter 6. Vector Calculus on Annuli""; ""1. Radial and spherical derivatives""; ""2. Some differential forms""; ""Chapter 7. Free Lagrangians""; ""Chapter 8. Some Estimates of Free Lagrangians""; ""1. The Fh-energy integral with operator norm""; ""2. Radial symmetry""; ""3. Proof of Theorem 1.14""""1. Extremal deformations of the sphere """"2. Random variable setting""; ""3. Pulling back a homothety via stereographic projection""; ""4. Back to the variational integral T[]""; ""5. The failure of radial symmetry, Proof of Theorem 1.11""; ""Chapter 15. Quasiconformal Mappings between Annuli""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 218, Number 1023.Quasiconformal mappingsExtremal problems (Mathematics)Quasiconformal mappings.Extremal problems (Mathematics)516.3/62Iwaniec Tadeusz66901Onninen Jani1973-MiAaPQMiAaPQMiAaPQBOOK9910788618103321N-harmonic mappings between annuli3796228UNINA