| Description |
1 online resource (xviii, 469 pages) |
| Series |
De Gruyter expositions in mathematics ; 55 |
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De Gruyter expositions in mathematics ; 55.
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| Contents |
880-01 Preface; Contents; Nomenclature; 1 Elements of Hilbert Space Theory; 2 Sobolev Lattices; 3 Linear Partial Differential Equations with Constant Coefficients; 4 Linear Evolution Equations; 5 Some Evolution Equations of Mathematical Physics; 6 A "Royal Road" to Initial Boundary Value Problems; Conclusion; Bibliography; Index |
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880-01/(S Machine generated contents note: 1. Elements of Hilbert Space Theory -- 1.1. Hilbert Space -- 1.2. Some Construction Principles of Hilbert Spaces -- 1.2.1. Direct Sums of Hilbert Spaces -- 1.2.2. Dual Spaces -- 1.2.3. Tensor Products of Hilbert Spaces -- 2. Sobolev Lattices -- 2.1. Sobolev Chains -- 2.2. Sobolev Lattices -- 2.3. Sobolev Lattices from Tensor Products of Sobolev Chains -- 3. Linear Partial Differential Equations with Constant Coefficients -- 3.1. Partial Differential Equations in H-[∞]([∂]ν + e) -- 3.1.1. First Steps Towards a Solution Theory -- 3.1.2. The Tarski-Seidenberg Theorem and some Consequences -- 3.1.3. Regularity Loss (0 ...,0) -- 3.1.4. Classification of Partial Differential Equations -- 3.1.5. The Classical Classification of Partial Differential Equations -- 3.1.6. Elliptic, Parabolic, Hyperbolic-- 3.1.7. Evolutionary Expressions in Canonical Form -- 3.1.8. Functions of [∂]ν and Convolutions -- 3.1.9. Systems and Scalar Equations |
| Summary |
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. Thefocus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. This global point of view is takenby focussing on the issues involved in determining the appropriate func |
| Bibliography |
Includes bibliographical references and index |
| Notes |
In English |
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Print version record |
| Subject |
Hilbert space.
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Differential equations, Partial.
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MATHEMATICS -- Transformations.
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Differential equations, Partial
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Hilbert space
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| Form |
Electronic book
|
| Author |
McGhee, D. F
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| ISBN |
9783110250275 |
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3110250276 |
|
1283399938 |
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9781283399937 |
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9786613399939 |
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6613399930 |
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