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 socalled 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 nonsmooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measurevalued 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 "integrationbyparts" in order to pass derivatives to smooth test functions by duality, is not available for nondivergence 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 EulerLagrange PDEReferences; 8 Existence of Viscosity Solutions to the Dirichlet Problem for the inftyLaplacian; References; 9 Miscellaneous Topics and Some Extensions of the Theory; 9.1 Fundamental Solutions of the inftyLaplacian; 9.1.1 The inftyLaplacian and TugofWar Differential Games; 9.1.2 Discontinuous Coefficients, Discontinuous Solutions; 9.1.3 BarlesPerthame Relaxed Limits (1Sided Uniform Convergence) and Generalised 1Sided Stability; 9.1.4 Boundary Jets and Jets Relative to Nonopen Sets
 9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the xvariable; 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 socalled 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 nonsmooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measurevalued 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 "integrationbyparts" in order to pass derivatives to smooth test functions by duality, is not available for nondivergence 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 EulerLagrange PDEReferences; 8 Existence of Viscosity Solutions to the Dirichlet Problem for the inftyLaplacian; References; 9 Miscellaneous Topics and Some Extensions of the Theory; 9.1 Fundamental Solutions of the inftyLaplacian; 9.1.1 The inftyLaplacian and TugofWar Differential Games; 9.1.2 Discontinuous Coefficients, Discontinuous Solutions; 9.1.3 BarlesPerthame Relaxed Limits (1Sided Uniform Convergence) and Generalised 1Sided Stability; 9.1.4 Boundary Jets and Jets Relative to Nonopen Sets
 9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the xvariable; 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
 10.1007/9783319128290
 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 EulerLagrange PDEReferences; 8 Existence of Viscosity Solutions to the Dirichlet Problem for the inftyLaplacian; References; 9 Miscellaneous Topics and Some Extensions of the Theory; 9.1 Fundamental Solutions of the inftyLaplacian; 9.1.1 The inftyLaplacian and TugofWar Differential Games; 9.1.2 Discontinuous Coefficients, Discontinuous Solutions; 9.1.3 BarlesPerthame Relaxed Limits (1Sided Uniform Convergence) and Generalised 1Sided Stability; 9.1.4 Boundary Jets and Jets Relative to Nonopen Sets
 9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the xvariable; 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
 10.1007/9783319128290
 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 faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Anintroductiontoviscositysolutionsforfully/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/Anintroductiontoviscositysolutionsforfully/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>