An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L
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An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L
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Author : Nikos Katzourakis
language : en
Publisher: Springer
Release Date : 2014-11-26
An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L written by Nikos Katzourakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-26 with Mathematics categories.
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.
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations
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Author : N. V. Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-07
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations written by N. V. Krylov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-07 with Differential equations, Parabolic categories.
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.
An Illustrative Introduction To Modern Analysis
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Author : Nikolaos Katzourakis
language : en
Publisher: CRC Press
Release Date : 2018-01-02
An Illustrative Introduction To Modern Analysis written by Nikolaos Katzourakis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Mathematics categories.
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
Viscosity Solutions And Applications
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Author : Martino Bardi
language : en
Publisher: Springer
Release Date : 2014-03-12
Viscosity Solutions And Applications written by Martino Bardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Mathematics categories.
The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.
Game Theory And Partial Differential Equations
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Author : Pablo Blanc
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-07-22
Game Theory And Partial Differential Equations written by Pablo Blanc and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher:
Release Date : 2018
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations written by Nikolaĭ Vladimirovich Krylov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
Notes On Tug Of War Games And The P Laplace Equation
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Author : Mikko Parviainen
language : en
Publisher: Springer Nature
Release Date :
Notes On Tug Of War Games And The P Laplace Equation written by Mikko Parviainen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Numerical Methods For Viscosity Solutions And Applications
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Author :
language : en
Publisher:
Release Date : 2006
Numerical Methods For Viscosity Solutions And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Viscosity Solutions And Optimal Control
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Author : Robert James Elliott
language : en
Publisher: Harlow, England : Longman Scientific & Technical
Release Date : 1987
Viscosity Solutions And Optimal Control written by Robert James Elliott and has been published by Harlow, England : Longman Scientific & Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Calculus of variations categories.
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications
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Author : Yves Achdou
language : en
Publisher: Springer
Release Date : 2013-05-24
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications written by Yves Achdou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).