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.
| Autorius: | Nikos Katzourakis |
| Serija: | SpringerBriefs in Mathematics |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2014 |
| Knygos puslapių skaičius: | 136 |
| ISBN-10: | 3319128280 |
| ISBN-13: | 9783319128283 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Differential calculus and equations |
Parašykite atsiliepimą apie „An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L¿“
