An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ electronic resource by Nikos Katzourakis.
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TextSeries: SpringerBriefs in MathematicsPublication details: Cham : Springer International Publishing : Imprint: Springer, 2015Description: XII, 123 p. 25 illus., 1 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319128290Subject(s): mathematics | Partial Differential Equations | Calculus of variations | Mathematics | Partial Differential Equations | Calculus of Variations and Optimal Control; OptimizationDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access online
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Springer eBooksSummary: 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.
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.
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