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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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| Format: | Printed Book |
| Language: | English |
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New York ; London :
Springer,
2011.
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| Series: | Universitext.
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Table of Contents:
- 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