Implicit Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1999
|
| Schriftenreihe: | Progress in Nonlinear Differential Equations and Their Applications
37 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nonlinear equations, particularly those of the second order, both linear and nonlinear and either in divergence or nondivergence form. Quasilinear and fully nonlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called "implicit partial differential equations", described in detail in the introduction (c.f. Chapter 1). It is a class of nonlinear equations that does not include the family of fully nonlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nonlin ear elasticity, problems of phase transitions and optimal design; some results have not been published elsewhere |
| Beschreibung: | 1 Online-Ressource (XIII, 273 p) |
| ISBN: | 9781461215622 9781461271932 |
| DOI: | 10.1007/978-1-4612-1562-2 |
Internformat
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1562-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461215622 9781461271932 |
| language | English |
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| spelling | Dacorogna, Bernard Verfasser aut Implicit Partial Differential Equations by Bernard Dacorogna, Paolo Marcellini Boston, MA Birkhäuser Boston 1999 1 Online-Ressource (XIII, 273 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 37 Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nonlinear equations, particularly those of the second order, both linear and nonlinear and either in divergence or nondivergence form. Quasilinear and fully nonlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called "implicit partial differential equations", described in detail in the introduction (c.f. Chapter 1). It is a class of nonlinear equations that does not include the family of fully nonlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nonlin ear elasticity, problems of phase transitions and optimal design; some results have not been published elsewhere Mathematics Differential equations, partial Numerical analysis Partial Differential Equations Numerical Analysis Mathematik Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s 1\p DE-604 Marcellini, Paolo Sonstige oth https://doi.org/10.1007/978-1-4612-1562-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dacorogna, Bernard Implicit Partial Differential Equations Mathematics Differential equations, partial Numerical analysis Partial Differential Equations Numerical Analysis Mathematik Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4128900-6 |
| title | Implicit Partial Differential Equations |
| title_auth | Implicit Partial Differential Equations |
| title_exact_search | Implicit Partial Differential Equations |
| title_full | Implicit Partial Differential Equations by Bernard Dacorogna, Paolo Marcellini |
| title_fullStr | Implicit Partial Differential Equations by Bernard Dacorogna, Paolo Marcellini |
| title_full_unstemmed | Implicit Partial Differential Equations by Bernard Dacorogna, Paolo Marcellini |
| title_short | Implicit Partial Differential Equations |
| title_sort | implicit partial differential equations |
| topic | Mathematics Differential equations, partial Numerical analysis Partial Differential Equations Numerical Analysis Mathematik Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Mathematics Differential equations, partial Numerical analysis Partial Differential Equations Numerical Analysis Mathematik Nichtlineare partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4612-1562-2 |
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