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)
Resource Information
The item An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (xii, 123 pages)
- 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
- Isbn
- 9783319128290
- 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
- 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
- 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)
- 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)
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/An-introduction-to-viscosity-solutions-for-fully/htE9Fq1AOSA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/An-introduction-to-viscosity-solutions-for-fully/htE9Fq1AOSA/">An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞, Nikos Katzourakis, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
