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The Resource An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book)

An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book)

Label
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞
Title
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞
Statement of responsibility
Nikos Katzourakis
Creator
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Katzourakis, Nikos
Dewey number
  • 515/.353
  • 510
Illustrations
illustrations
Index
no index present
LC call number
QA377
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
SpringerBriefs in Mathematics,
http://library.link/vocab/subjectName
  • Differential equations, Partial
  • Differential equations, Nonlinear
  • Calculus of variations
Label
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book)
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • 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
  • 9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the x-variable; References
Control code
SPR897377020
Dimensions
unknown
Extent
1 online resource (xii, 123 pages)
File format
unknown
Form of item
online
Isbn
9783319128290
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-12829-0
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote
Label
An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book)
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • 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
  • 9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the x-variable; References
Control code
SPR897377020
Dimensions
unknown
Extent
1 online resource (xii, 123 pages)
File format
unknown
Form of item
online
Isbn
9783319128290
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-12829-0
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote

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