Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1995
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective. Chapter I is focused on the Cauchy-Kowaleski theorem. We discuss the notion of characteristic surfaces and use it to classify partial differential equations. The discussion grows out of equations of second order in two variables to equations of second order in N variables to p.d.e.'s of any order in N variables. In Chapters II and III we study the Laplace equation and connected elliptic theory. The existence of solutions for the Dirichlet problem is proven by the Perron method. This method clarifies the structure ofthe sub(super)harmonic functions and is closely related to the modern notion of viscosity solution. The elliptic theory is complemented by the Harnack and Liouville theorems, the simplest version of Schauder's estimates and basic LP -potential estimates. Then, in Chapter III, the Dirichlet and Neumann problems, as well as eigenvalue problems for the Laplacian, are cast in terms of integral equations. This requires some basic facts concerning double layer potentials and the notion of compact subsets of LP, which we present |
| Beschreibung: | 1 Online-Ressource (XIV, 416 p) |
| ISBN: | 9781489928405 9781489928429 |
| DOI: | 10.1007/978-1-4899-2840-5 |
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| 500 | |a This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective. Chapter I is focused on the Cauchy-Kowaleski theorem. We discuss the notion of characteristic surfaces and use it to classify partial differential equations. The discussion grows out of equations of second order in two variables to equations of second order in N variables to p.d.e.'s of any order in N variables. In Chapters II and III we study the Laplace equation and connected elliptic theory. The existence of solutions for the Dirichlet problem is proven by the Perron method. This method clarifies the structure ofthe sub(super)harmonic functions and is closely related to the modern notion of viscosity solution. The elliptic theory is complemented by the Harnack and Liouville theorems, the simplest version of Schauder's estimates and basic LP -potential estimates. Then, in Chapter III, the Dirichlet and Neumann problems, as well as eigenvalue problems for the Laplacian, are cast in terms of integral equations. This requires some basic facts concerning double layer potentials and the notion of compact subsets of LP, which we present | ||
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Datensatz im Suchindex
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4899-2840-5 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781489928405 9781489928429 |
| language | English |
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| spelling | DiBenedetto, Emmanuele Verfasser aut Partial Differential Equations by Emmanuele DiBenedetto Boston, MA Birkhäuser Boston 1995 1 Online-Ressource (XIV, 416 p) txt rdacontent c rdamedia cr rdacarrier This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective. Chapter I is focused on the Cauchy-Kowaleski theorem. We discuss the notion of characteristic surfaces and use it to classify partial differential equations. The discussion grows out of equations of second order in two variables to equations of second order in N variables to p.d.e.'s of any order in N variables. In Chapters II and III we study the Laplace equation and connected elliptic theory. The existence of solutions for the Dirichlet problem is proven by the Perron method. This method clarifies the structure ofthe sub(super)harmonic functions and is closely related to the modern notion of viscosity solution. The elliptic theory is complemented by the Harnack and Liouville theorems, the simplest version of Schauder's estimates and basic LP -potential estimates. Then, in Chapter III, the Dirichlet and Neumann problems, as well as eigenvalue problems for the Laplacian, are cast in terms of integral equations. This requires some basic facts concerning double layer potentials and the notion of compact subsets of LP, which we present Mathematics Differential equations, partial Partial Differential Equations Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Partielle Differentialgleichung (DE-588)4044779-0 s 2\p DE-604 https://doi.org/10.1007/978-1-4899-2840-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | DiBenedetto, Emmanuele Partial Differential Equations Mathematics Differential equations, partial Partial Differential Equations Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4123623-3 |
| title | Partial Differential Equations |
| title_auth | Partial Differential Equations |
| title_exact_search | Partial Differential Equations |
| title_full | Partial Differential Equations by Emmanuele DiBenedetto |
| title_fullStr | Partial Differential Equations by Emmanuele DiBenedetto |
| title_full_unstemmed | Partial Differential Equations by Emmanuele DiBenedetto |
| title_short | Partial Differential Equations |
| title_sort | partial differential equations |
| topic | Mathematics Differential equations, partial Partial Differential Equations Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematics Differential equations, partial Partial Differential Equations Mathematik Partielle Differentialgleichung Lehrbuch |
| url | https://doi.org/10.1007/978-1-4899-2840-5 |
| work_keys_str_mv | AT dibenedettoemmanuele partialdifferentialequations |