TY  - BOOK
AU  - Katzourakis,Nikos
ED  - SpringerLink (Online service)
TI  - An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
T2  - SpringerBriefs in Mathematics,
SN  - 9783319128290
AV  - QA370-380 
U1  - 515.353 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Partial differential equations
KW  - Calculus of variations
KW  - Partial Differential Equations
KW  - Calculus of Variations and Optimal Control; Optimization
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-12829-0
ER  -