Annales academiae scientiarum fennica. Mathematica dissertationes; 160: Lindberg S. On the Jacobian equation and the Hardy space H1(C) (Helsinki, 2015). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаAnnales academiæ scientiarum Fennicæ. Mathematica dissertationes. 160: Lindberg S. On the Jacobian equation and the Hardy space H1(C) / Suomalainen tiedeakatemia (Helsinki). - Helsinki: Suomalainen tiedeakatemia, 2015. - 64 p.: ill. - Bibliogr.: p.62-64. - ISBN 978-951-41-1076-4; ISSN 1239-6303
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
1  Introduction ................................................. 5
2  Preliminaries ............................................... 13
   2.1  Sobolev spaces ......................................... 13
   2.2  Invertibility of Sobolev mappings ...................... 14
   2.3  The Hardy space fig.21(fig.1) ................................. 15
   2.4  Jacobians of Sobolev mappings .......................... 17
   2.5  VMO(fig.1) and BMO(fig.1) ..................................... 18
   2.6  The Cauchy transform and the Beurling transform ........ 20
   2.7  Commutators ............................................ 21
   2.8  An equivalent norm in BMO(fig.1) ........................... 22
   2.9  Banach spaces .......................................... 24
3  The Jacobian Equation with Radial Data ...................... 26
   3.1  Radial stretchings as solutions ........................ 26
   3.2  Generalized radially symmetric solutions ............... 31
4  Energy-Minimal Solutions and Lagrange Multipliers ........... 35
   4.1  Energy-minimal solutions ............................... 35
   4.2  Lagrange multipliers ................................... 37
   4.3  Operator theoretical treatment of Lagrange
        multipliers ............................................ 38
5  On the Existence of Lagrange Multipliers .................... 39
   5.1  The norm ||•|| bmos and Lagrange multipliers ........... 39
   5.2  Lagrange multipliers in VMOS(fig.1) ....................... 40
   5.3  Characterizations of the norms ||•||BMOS and ||•||H1S ... 41
   5.4  Connection to commutators ............................. 42
6  On the Class fig.3L2S ........................................... 44
   6.1  Topological properties of {|Sƒ|2 - |ƒ|2 : ƒ ϵ fig.3L2S} ..... 44
   6.2  Extreme points of fig.4H1S ................................. 45
   6.3  The duality mapping D: fig.3VMOSfig.3H1S ..................... 45
7  Local Study of Energy-Minimal Solutions and Lagrange
   Multipliers ................................................. 48
   7.1  Lagrange multipliers in a bounded domain ............... 48
   7.2  Smooth, compactly supported Lagrange multipliers ....... 51
8  Behavior of Solutions in Domains Where the Jacobian
   Vanishes .................................................... 54
   8.1  The Hopf-Laplace equation .............................. 54
   8.2  Harmonicity of solutions ............................... 56
   8.3  Solution of a problem of Lou, Yang and Song ............ 58
   References .................................................. 62


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