An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutio...
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| Ngôn ngữ: | English |
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Springer
2015
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57843 |
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oai:scholar.dlu.edu.vn:DLU123456789-578432023-11-11T05:55:21Z An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ Katzourakis, Nikos Partial Differential equations Nonlinear Calculus of variations The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE. 2015-08-31T03:25:15Z 2015-08-31T03:25:15Z 2015 Book 978-3-319-12829-0 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57843 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Partial Differential equations Nonlinear Calculus of variations |
| spellingShingle |
Partial Differential equations Nonlinear Calculus of variations Katzourakis, Nikos An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |
| description |
The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE. |
| format |
Book |
| author |
Katzourakis, Nikos |
| author_facet |
Katzourakis, Nikos |
| author_sort |
Katzourakis, Nikos |
| title |
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |
| title_short |
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |
| title_full |
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |
| title_fullStr |
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |
| title_full_unstemmed |
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ |
| title_sort |
introduction to viscosity solutions for fully nonlinear pde with applications to calculus of variations in l∞ |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57843 |
| _version_ |
1819803489828601856 |