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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Hlavní autor: Brézis, H.
Médium: Printed Book
Jazyk:English
Vydáno: New York ; London : Springer, 2011.
Edice:Universitext.
Témata:
Functional analysis.
Differential equations, Partial.
Sobolev spaces.
Obsah:
  • The Hahn-Banach theorems : introduction to the theory of conjugate convex functions
  • The uniform boundedness principle and the closed graph theorem
  • Weak topologies, reflexive spaces, separable spaces, uniform convexity
  • Lp spaces
  • Hilbert spaces
  • Compact operators, spectral decomposition of self-adjoint compact operators
  • The Hille-Yosida theorem
  • Sobolev spaces and the variational formulation of boundary value problems in one dimension
  • Sobolev spaces and the variational formulation of elliptic boundary value problems in N dimensions
  • Evolution problems : the heat equation and the wave equation
  • Miscellaneous complements

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