Functional Analysis, Sobolev Spaces and Partial Differential Equations

Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct "worlds," functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth trans...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Brezis, Haim (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2011.
Edición:1st ed. 2011.
Colección:Universitext,
Temas:
Functional analysis.
Differential equations.
Difference equations.
Functional equations.
Functional Analysis.
Differential Equations.
Difference and Functional Equations.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preface
  • 1. The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions
  • 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators
  • 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity
  • 4. L^p Spaces
  • 5. Hilbert Spaces
  • 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators
  • 7. The Hille-Yosida Theorem
  • 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension
  • 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions
  • 10. Evolution Problems: The Heat Equation and the Wave Equation
  • 11. Some Complements
  • Problems
  • Solutions of Some Exercises and Problems
  • Bibliography
  • Index.

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