Partial differential equations :: a unified Hilbert space approach /
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 se...
Gespeichert in:
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
De Gruyter,
©2011.
|
| Schriftenreihe: | De Gruyter expositions in mathematics ;
55. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xviii, 469 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110250275 3110250276 1283399938 9781283399937 9786613399939 6613399930 |
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| 245 | 1 | 0 | |a Partial differential equations : |b a unified Hilbert space approach / |c Rainer Picard, Des McGhee. |
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| 505 | 0 | |6 880-01 |a 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. | |
| 520 | |a 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. | ||
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| author | Picard, R. H. (Rainer H.) |
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| contents | 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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| discipline | Mathematik |
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| indexdate | 2024-11-27T13:18:00Z |
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| series | De Gruyter expositions in mathematics ; |
| series2 | De Gruyter expositions in mathematics ; |
| spelling | Picard, R. H. (Rainer H.) https://id.oclc.org/worldcat/entity/E39PBJv8CcvvrxxHJvhkX9WhpP http://id.loc.gov/authorities/names/n88033139 Partial differential equations : a unified Hilbert space approach / Rainer Picard, Des McGhee. Berlin ; New York : De Gruyter, ©2011. 1 online resource (xviii, 469 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter expositions in mathematics ; 55 Includes bibliographical references and index. Print version record. 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. 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. In English. Hilbert space. http://id.loc.gov/authorities/subjects/sh85060803 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Differential equations, Partial. Equations. Hilbert space. Espace de Hilbert. Équations aux dérivées partielles. MATHEMATICS Transformations. bisacsh Differential equations, Partial fast Hilbert space fast McGhee, D. F. has work: Partial differential equations (Text) https://id.oclc.org/worldcat/entity/E39PCGtvbTKfkdKGQ3jWFVGTH3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Picard, R.H. (Rainer H.). Partial differential equations. Berlin ; New York : De Gruyter, ©2011 9783110250268 (DLC) 2011004423 (OCoLC)705567992 De Gruyter expositions in mathematics ; 55. http://id.loc.gov/authorities/names/n90653843 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=381760 Volltext 505-01/(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. |
| spellingShingle | Picard, R. H. (Rainer H.) Partial differential equations : a unified Hilbert space approach / De Gruyter expositions in mathematics ; 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. Hilbert space. http://id.loc.gov/authorities/subjects/sh85060803 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Differential equations, Partial. Equations. Hilbert space. Espace de Hilbert. Équations aux dérivées partielles. MATHEMATICS Transformations. bisacsh Differential equations, Partial fast Hilbert space fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85060803 http://id.loc.gov/authorities/subjects/sh85037912 |
| title | Partial differential equations : a unified Hilbert space approach / |
| title_auth | Partial differential equations : a unified Hilbert space approach / |
| title_exact_search | Partial differential equations : a unified Hilbert space approach / |
| title_full | Partial differential equations : a unified Hilbert space approach / Rainer Picard, Des McGhee. |
| title_fullStr | Partial differential equations : a unified Hilbert space approach / Rainer Picard, Des McGhee. |
| title_full_unstemmed | Partial differential equations : a unified Hilbert space approach / Rainer Picard, Des McGhee. |
| title_short | Partial differential equations : |
| title_sort | partial differential equations a unified hilbert space approach |
| title_sub | a unified Hilbert space approach / |
| topic | Hilbert space. http://id.loc.gov/authorities/subjects/sh85060803 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Differential equations, Partial. Equations. Hilbert space. Espace de Hilbert. Équations aux dérivées partielles. MATHEMATICS Transformations. bisacsh Differential equations, Partial fast Hilbert space fast |
| topic_facet | Hilbert space. Differential equations, Partial. Equations. Espace de Hilbert. Équations aux dérivées partielles. MATHEMATICS Transformations. Differential equations, Partial Hilbert space |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=381760 |
| work_keys_str_mv | AT picardrh partialdifferentialequationsaunifiedhilbertspaceapproach AT mcgheedf partialdifferentialequationsaunifiedhilbertspaceapproach |