An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
Katzourakis, Nikos.
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ [electronic resource] / by Nikos Katzourakis. - XII, 123 p. 25 illus., 1 illus. in color. online resource. - SpringerBriefs in Mathematics, 2191-8198 . - SpringerBriefs in Mathematics, .
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.
9783319128290
10.1007/978-3-319-12829-0 doi
Mathematics.
Partial differential equations.
Calculus of variations.
Mathematics.
Partial Differential Equations.
Calculus of Variations and Optimal Control; Optimization.
QA370-380
515.353
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ [electronic resource] / by Nikos Katzourakis. - XII, 123 p. 25 illus., 1 illus. in color. online resource. - SpringerBriefs in Mathematics, 2191-8198 . - SpringerBriefs in Mathematics, .
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.
9783319128290
10.1007/978-3-319-12829-0 doi
Mathematics.
Partial differential equations.
Calculus of variations.
Mathematics.
Partial Differential Equations.
Calculus of Variations and Optimal Control; Optimization.
QA370-380
515.353