Semiconcave functions, Hamilton-Jacobi equations, and optimal control
type: Item
instance of: scholarly article
title: Semiconcave functions, Hamilton-Jacobi equations, and optimal control
zbMATH Open document ID: 1095.49003
author: Piermarco Cannarsa
author: Carlo Sinestrari
published in: Progress in Nonlinear Differential Equations and Their Applications
publication date: 2005-01-19T00:00:00Z
review text: This book is the first systematic and comprehensive study of the theory of semiconcave functions. The book consists of 6 Chapters and an Appendix. The Chapter 1 is introductory to the whole text. There is studied a model problem from the calculus variations: this allows to present, in a simple situation, some of the main ideas, that will be developed in the rest of the book. In the Chapters 2, 3 and 4 the theory of semiconcave functions without aiming at specific application is developed. In the Chapters 5,6,7 and 8 the authors discuss contexts in which semiconcavity plays an important role such as Hamilton-Jacobi equation, calculus of variations, optimal control theory. In the Appendix all the needed definitions and most proofs of the basic results are presented. Researchers in optimal control, the calculus of variations, and partial differential equations will find this book useful as a state-of-the-art reference for semiconcave functions.
reviewed by: A. A. Tolstonogov
Mathematics Subject Classification ID: 49-02
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49L25
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 2129788
zbMATH Keywords: semiconcave function
zbMATH Keywords: calculus of variations
zbMATH Keywords: generalized gradients
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: viscosity solutions
zbMATH Keywords: Mayer problem
zbMATH Keywords: Bolza problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2129788