An introduction to maximum principles and symmetry in elliptic problems:
Originally published in 2000, this was the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2000
|
| Series: | Cambridge tracts in mathematics
128 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Originally published in 2000, this was the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. Results are presented with minimal prerequisites in a style suited to graduate students. Two long and leisurely appendices give basic facts about the Laplace and Poisson equations. There is a plentiful supply of exercises, with detailed hints |
| Physical Description: | 1 Online-Ressource (x, 340 Seiten) |
| ISBN: | 9780511569203 |
| DOI: | 10.1017/CBO9780511569203 |
Staff View
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| 520 | |a Originally published in 2000, this was the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. Results are presented with minimal prerequisites in a style suited to graduate students. Two long and leisurely appendices give basic facts about the Laplace and Poisson equations. There is a plentiful supply of exercises, with detailed hints | ||
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Record in the Search Index
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| any_adam_object | |
| author | Fraenkel, L. Edward 1927-2019 |
| author_GND | (DE-588)143989944 |
| author_facet | Fraenkel, L. Edward 1927-2019 |
| author_role | aut |
| author_sort | Fraenkel, L. Edward 1927-2019 |
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| bvnumber | BV043941611 |
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| contents | Some Notation, Terminology and Basic Calculus -- 1. Introduction -- 2. Some Maximum Principles for Elliptic Equations -- 3. Symmetry for a Non-linear Poisson Equation in a Symmetric Set [Omega] -- 4. Symmetry for the Non-linear Poisson Equation in R[superscript N] -- 5. Monotonicity of Positive Solutions in a Bounded Set [Omega] -- App. A. On the Newtonian Potential -- App. B. Rudimentary Facts about Harmonic Functions and the Poisson Equation -- App. C. Construction of the Primary Function of Siegel Type -- App. D. On the Divergence Theorem and Related Matters -- App. E. The Edge-Point Lemma |
| ctrlnum | (ZDB-20-CBO)CR9780511569203 (OCoLC)850670710 (DE-599)BVBBV043941611 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511569203 |
| format | Electronic eBook |
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| id | DE-604.BV043941611 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511569203 |
| language | English |
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| physical | 1 Online-Ressource (x, 340 Seiten) |
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| publishDate | 2000 |
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| spelling | Fraenkel, L. Edward 1927-2019 Verfasser (DE-588)143989944 aut An introduction to maximum principles and symmetry in elliptic problems L.E. Fraenkel An Introduction to Maximum Principles & Symmetry in Elliptic Problems Cambridge Cambridge University Press 2000 1 Online-Ressource (x, 340 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 128 Some Notation, Terminology and Basic Calculus -- 1. Introduction -- 2. Some Maximum Principles for Elliptic Equations -- 3. Symmetry for a Non-linear Poisson Equation in a Symmetric Set [Omega] -- 4. Symmetry for the Non-linear Poisson Equation in R[superscript N] -- 5. Monotonicity of Positive Solutions in a Bounded Set [Omega] -- App. A. On the Newtonian Potential -- App. B. Rudimentary Facts about Harmonic Functions and the Poisson Equation -- App. C. Construction of the Primary Function of Siegel Type -- App. D. On the Divergence Theorem and Related Matters -- App. E. The Edge-Point Lemma Originally published in 2000, this was the first book to present the basic theory of the symmetry of solutions to second-order elliptic partial differential equations by means of the maximum principle. It proceeds from elementary facts about the linear case to recent results about positive solutions of non-linear elliptic equations. Gidas, Ni and Nirenberg, building on work of Alexandrov and of Serrin, have shown that the shape of the set on which such elliptic equations are solved has a strong effect on the form of positive solutions. In particular, if the equation and its boundary condition allow spherically symmetric solutions, then, remarkably, all positive solutions are spherically symmetric. Results are presented with minimal prerequisites in a style suited to graduate students. Two long and leisurely appendices give basic facts about the Laplace and Poisson equations. There is a plentiful supply of exercises, with detailed hints Differential equations, Elliptic Maximum principles (Mathematics) Differential equations, Elliptic / Problems, exercises, etc Symmetry Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Maximumprinzip (DE-588)4169165-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Symmetrie (DE-588)4058724-1 s Maximumprinzip (DE-588)4169165-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-46195-5 Erscheint auch als Druck-Ausgabe 978-0-521-17278-3 https://doi.org/10.1017/CBO9780511569203 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Fraenkel, L. Edward 1927-2019 An introduction to maximum principles and symmetry in elliptic problems Some Notation, Terminology and Basic Calculus -- 1. Introduction -- 2. Some Maximum Principles for Elliptic Equations -- 3. Symmetry for a Non-linear Poisson Equation in a Symmetric Set [Omega] -- 4. Symmetry for the Non-linear Poisson Equation in R[superscript N] -- 5. Monotonicity of Positive Solutions in a Bounded Set [Omega] -- App. A. On the Newtonian Potential -- App. B. Rudimentary Facts about Harmonic Functions and the Poisson Equation -- App. C. Construction of the Primary Function of Siegel Type -- App. D. On the Divergence Theorem and Related Matters -- App. E. The Edge-Point Lemma Differential equations, Elliptic Maximum principles (Mathematics) Differential equations, Elliptic / Problems, exercises, etc Symmetry Elliptische Differentialgleichung (DE-588)4014485-9 gnd Symmetrie (DE-588)4058724-1 gnd Maximumprinzip (DE-588)4169165-9 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4058724-1 (DE-588)4169165-9 |
| title | An introduction to maximum principles and symmetry in elliptic problems |
| title_alt | An Introduction to Maximum Principles & Symmetry in Elliptic Problems |
| title_auth | An introduction to maximum principles and symmetry in elliptic problems |
| title_exact_search | An introduction to maximum principles and symmetry in elliptic problems |
| title_full | An introduction to maximum principles and symmetry in elliptic problems L.E. Fraenkel |
| title_fullStr | An introduction to maximum principles and symmetry in elliptic problems L.E. Fraenkel |
| title_full_unstemmed | An introduction to maximum principles and symmetry in elliptic problems L.E. Fraenkel |
| title_short | An introduction to maximum principles and symmetry in elliptic problems |
| title_sort | an introduction to maximum principles and symmetry in elliptic problems |
| topic | Differential equations, Elliptic Maximum principles (Mathematics) Differential equations, Elliptic / Problems, exercises, etc Symmetry Elliptische Differentialgleichung (DE-588)4014485-9 gnd Symmetrie (DE-588)4058724-1 gnd Maximumprinzip (DE-588)4169165-9 gnd |
| topic_facet | Differential equations, Elliptic Maximum principles (Mathematics) Differential equations, Elliptic / Problems, exercises, etc Symmetry Elliptische Differentialgleichung Symmetrie Maximumprinzip |
| url | https://doi.org/10.1017/CBO9780511569203 |
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