Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1989
|
| Schriftenreihe: | Graduate Texts in Mathematics
120 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The term "weakly differentiable functions" in the title refers to those integrable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV functions), have undergone considerable development during the past 20 years. From this development a rather complete theory has emerged and thus has provided the main impetus for the writing of this book. Since these classes of functions play a significant role in many fields, such as approximation theory, calculus of variations, partial differential equations, and non-linear potential theory, it is hoped that this monograph will be of assistance to a wide range of graduate students and researchers in these and perhaps other related areas. Some of the material in Chapters 1-4 has been presented in a graduate course at Indiana University during the 1987-88 academic year, and I am indebted to the students and colleagues in attendance for their helpful comments and suggestions |
| Beschreibung: | 1 Online-Ressource (XVI, 308 p) |
| ISBN: | 9781461210153 9781461269854 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-1015-3 |
Internformat
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Datensatz im Suchindex
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| institution | BVB |
| isbn | 9781461210153 9781461269854 |
| issn | 0072-5285 |
| language | English |
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| spelling | Ziemer, William P. Verfasser aut Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation by William P. Ziemer New York, NY Springer New York 1989 1 Online-Ressource (XVI, 308 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 120 0072-5285 The term "weakly differentiable functions" in the title refers to those integrable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV functions), have undergone considerable development during the past 20 years. From this development a rather complete theory has emerged and thus has provided the main impetus for the writing of this book. Since these classes of functions play a significant role in many fields, such as approximation theory, calculus of variations, partial differential equations, and non-linear potential theory, it is hoped that this monograph will be of assistance to a wide range of graduate students and researchers in these and perhaps other related areas. Some of the material in Chapters 1-4 has been presented in a graduate course at Indiana University during the 1987-88 academic year, and I am indebted to the students and colleagues in attendance for their helpful comments and suggestions Mathematics Potential theory (Mathematics) Potential Theory Mathematik Funktion von beschränkter Variation (DE-588)4155666-5 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 s 1\p DE-604 Funktion von beschränkter Variation (DE-588)4155666-5 s 2\p DE-604 Graduate Texts in Mathematics 120 (DE-604)BV035421258 120 https://doi.org/10.1007/978-1-4612-1015-3 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 | Ziemer, William P. Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation Graduate Texts in Mathematics Mathematics Potential theory (Mathematics) Potential Theory Mathematik Funktion von beschränkter Variation (DE-588)4155666-5 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4155666-5 (DE-588)4055345-0 |
| title | Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation |
| title_auth | Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation |
| title_exact_search | Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation |
| title_full | Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation by William P. Ziemer |
| title_fullStr | Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation by William P. Ziemer |
| title_full_unstemmed | Weakly Differentiable Functions Sobolev Spaces and Functions of Bounded Variation by William P. Ziemer |
| title_short | Weakly Differentiable Functions |
| title_sort | weakly differentiable functions sobolev spaces and functions of bounded variation |
| title_sub | Sobolev Spaces and Functions of Bounded Variation |
| topic | Mathematics Potential theory (Mathematics) Potential Theory Mathematik Funktion von beschränkter Variation (DE-588)4155666-5 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Mathematics Potential theory (Mathematics) Potential Theory Mathematik Funktion von beschränkter Variation Sobolev-Raum |
| url | https://doi.org/10.1007/978-1-4612-1015-3 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT ziemerwilliamp weaklydifferentiablefunctionssobolevspacesandfunctionsofboundedvariation |