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Author : Yi Zhan
Release : 2000
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Viscosity Solutions of Nonlinear Degenerate Parabolic Equations and Several Applications by : Yi Zhan
Download or read book Viscosity Solutions of Nonlinear Degenerate Parabolic Equations and Several Applications written by Yi Zhan. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Release : 2000
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Viscosity Solutions of Nonlinear Degenerate Parabolic Equations and Several Applications by :
Download or read book Viscosity Solutions of Nonlinear Degenerate Parabolic Equations and Several Applications written by . This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nikos Katzourakis
Release : 2014-11-26
Genre : Mathematics
Kind : eBook
Book Rating : 299/5 ( reviews)
Book Synopsis An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ by : Nikos Katzourakis
Download or read book An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ written by Nikos Katzourakis. This book was released on 2014-11-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : N. V. Krylov
Release : 2018-09-07
Genre : Mathematics
Kind : eBook
Book Rating : 401/5 ( reviews)
Book Synopsis Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations by : N. V. Krylov
Download or read book Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations written by N. V. Krylov. This book was released on 2018-09-07. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.
Author : Nikolaĭ Vladimirovich Krylov
Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 69X/5 ( reviews)
Book Synopsis Lectures on Elliptic and Parabolic Equations in Holder Spaces by : Nikolaĭ Vladimirovich Krylov
Download or read book Lectures on Elliptic and Parabolic Equations in Holder Spaces written by Nikolaĭ Vladimirovich Krylov. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
