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Modern Methods in the Calculus of Variations: Lp Spaces

Irene Fonseca Giovanni Leoni

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-35784-3

ISBN electrónico

978-0-387-69006-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, LLC 2007

Cobertura temática

matematica

Matemáticas

fisica

Ciencias físicas

Tabla de contenidos

doi: 10.1007/978-0-387-69006-3_1

Measures

Irene Fonseca; Giovanni Leoni

This chapter covers a wide range of properties of measures. Those that we consider basic and well known (for example the Lebesgue dominated convergence theorem) will only be stated, and the reader is referred to classical textbooks such as [DB02], [EvGa92], [Fol99], [Rao04], [Ru87], [Z67]. The reader should be warned that in some of these books outer measures are called measures.

1 - Measure Theory and Lp Spaces | Pp. 3-138

doi: 10.1007/978-0-387-69006-3_2

Lp Spaces

Irene Fonseca; Giovanni Leoni

In this section we introduce the spaces and study their properties. Proofs of standard results, such as Hölder’s and Minkowski’s inequalities, will be omitted, and we refer the reader to [Bar95], [DB02], [DuSc88], [EvGa92], [Fol99], [Rao04], [Ru87].

1 - Measure Theory and Lp Spaces | Pp. 139-228

doi: 10.1007/978-0-387-69006-3_3

The Direct Method and Lower Semicontinuity

Irene Fonseca; Giovanni Leoni

This chapter covers a wide range of properties of measures. Those that we consider basic and well known (for example the Lebesgue dominated convergence theorem) will only be stated, and the reader is referred to classical textbooks such as [DB02], [EvGa92], [Fol99], [Rao04], [Ru87], [Z67]. The reader should be warned that in some of these books outer measures are called measures.

2 - The Direct Method and Lower Semicontinuity | Pp. 231-246

doi: 10.1007/978-0-387-69006-3_4

ConvexAnalysis

Irene Fonseca; Giovanni Leoni

This chapter covers a wide range of properties of measures. Those that we consider basic and well known (for example the Lebesgue dominated convergence theorem) will only be stated, and the reader is referred to classical textbooks such as [DB02], [EvGa92], [Fol99], [Rao04], [Ru87], [Z67]. The reader should be warned that in some of these books outer measures are called measures.

2 - The Direct Method and Lower Semicontinuity | Pp. 247-321

doi: 10.1007/978-0-387-69006-3_5

Integrands f = f (z)

Irene Fonseca; Giovanni Leoni

This chapter covers a wide range of properties of measures. Those that we consider basic and well known (for example the Lebesgue dominated convergence theorem) will only be stated, and the reader is referred to classical textbooks such as [DB02], [EvGa92], [Fol99], [Rao04], [Ru87], [Z67]. The reader should be warned that in some of these books outer measures are called measures.

3 - Functionals Defined on Lp | Pp. 325-378

doi: 10.1007/978-0-387-69006-3_6

Integrands f = f (x, z)

Irene Fonseca; Giovanni Leoni

In this section we introduce the spaces and study their properties. Proofs of standard results, such as Hölder’s and Minkowski’s inequalities, will be omitted, and we refer the reader to [Bar95], [DB02], [DuSc88], [EvGa92], [Fol99], [Rao04], [Ru87].

3 - Functionals Defined on Lp | Pp. 379-484

doi: 10.1007/978-0-387-69006-3_7

Integrands f = f (x, u, z)

Irene Fonseca; Giovanni Leoni

This chapter covers a wide range of properties of measures. Those that we consider basic and well known (for example the Lebesgue dominated convergence theorem) will only be stated, and the reader is referred to classical textbooks such as [DB02], [EvGa92], [Fol99], [Rao04], [Ru87], [Z67]. The reader should be warned that in some of these books outer measures are called measures.

3 - Functionals Defined on Lp | Pp. 485-515

doi: 10.1007/978-0-387-69006-3_8

Young Measures

Irene Fonseca; Giovanni Leoni

This chapter covers a wide range of properties of measures. Those that we consider basic and well known (for example the Lebesgue dominated convergence theorem) will only be stated, and the reader is referred to classical textbooks such as [DB02], [EvGa92], [Fol99], [Rao04], [Ru87], [Z67]. The reader should be warned that in some of these books outer measures are called measures.

3 - Functionals Defined on Lp | Pp. 517-545