An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ /
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| Author / Creator: | Katzourakis, Nikos, author. |
|---|---|
| Imprint: | Cham : Springer, 2015. |
| Description: | 1 online resource (xii, 123 pages) : illustrations (some color). |
| Language: | English |
| Series: | SpringerBriefs in Mathematics, 2191-8198 SpringerBriefs in mathematics. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11090159 |
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| 100 | 1 | |a Katzourakis, Nikos, |e author. |0 http://id.loc.gov/authorities/names/no2015040373 |1 http://viaf.org/viaf/315189964 | |
| 245 | 1 | 3 | |a An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ / |c Nikos Katzourakis. |
| 264 | 1 | |a Cham : |b Springer, |c 2015. | |
| 300 | |a 1 online resource (xii, 123 pages) : |b illustrations (some color). | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a SpringerBriefs in Mathematics, |x 2191-8198 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed February 3, 2015). | |
| 520 | |a 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. | ||
| 505 | 0 | |a Preface; Acknowledgments; Contents; 1 History, Examples, Motivation and First Definitions; References; 2 Second Definitions and Basic Analytic Properties of the Notions; References; 3 Stability Properties of the Notions and Existence via Approximation; References; 4 Mollification of Viscosity Solutions and Semiconvexity; References; 5 Existence of Solution to the Dirichlet Problem via Perron's Method; References; 6 Comparison Results and Uniqueness of Solution to the Dirichlet Problem; References | |
| 505 | 8 | |a 7 Minimisers of Convex Functionals and Existence of Viscosity Solutions to the Euler-Lagrange PDEReferences; 8 Existence of Viscosity Solutions to the Dirichlet Problem for the infty-Laplacian; References; 9 Miscellaneous Topics and Some Extensions of the Theory; 9.1 Fundamental Solutions of the infty-Laplacian; 9.1.1 The infty-Laplacian and Tug-of-War Differential Games; 9.1.2 Discontinuous Coefficients, Discontinuous Solutions; 9.1.3 Barles-Perthame Relaxed Limits (1-Sided Uniform Convergence) and Generalised 1-Sided Stability; 9.1.4 Boundary Jets and Jets Relative to Non-open Sets | |
| 505 | 8 | |a 9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the x-variable; References | |
| 650 | 0 | |a Differential equations, Partial. |0 http://id.loc.gov/authorities/subjects/sh85037912 | |
| 650 | 0 | |a Differential equations, Nonlinear. |0 http://id.loc.gov/authorities/subjects/sh85037906 | |
| 650 | 0 | |a Calculus of variations. |0 http://id.loc.gov/authorities/subjects/sh85018809 | |
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 2 | 4 | |a Partial Differential Equations. |
| 650 | 2 | 4 | |a Calculus of Variations and Optimal Control; Optimization. |
| 650 | 7 | |a Calculus of variations. |2 fast |0 (OCoLC)fst00844140 | |
| 650 | 7 | |a Differential equations, Nonlinear. |2 fast |0 (OCoLC)fst00893474 | |
| 650 | 7 | |a Differential equations, Partial. |2 fast |0 (OCoLC)fst00893484 | |
| 650 | 1 | 2 | |a Mathematics. |
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| 655 | 0 | |a Electronic books. | |
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