論文の公開元へ

書き出し

Refer/BibIX

RIS

BibTeX

TSV

EIKONAL EQUATIONS ON METRIC SPACES (Women in Mathematics)

ZHOU, XIAODAN 京都大学

2023.04

概要

Given an equation |∇u|= 1, how do we solve it? What kind of functions should we call it the solutions to this so-called eikonal equation? In this talk, we will focus on this simple equation, a special case of the Hamilton-Jacobi equation. The Hamilton-Jacobi equation in general metric spaces recently attracts a great deal of attention because of its broad applications in optimal transport, traffic flow, networks, etc. We will first give a review of basic results of eikonal equation in the Euclidean space and introduce some recent development of this equation on metric spaces.

論文の公開元へ

この論文で使われている画像

参考文献

[AF] L. Ambrosio and J. Feng. On a class of first order Hamilton-Jacobi equations in metric spaces. J. Differential

Equations, 256(7):2194-2245, 2014.

[BC] M. Bardi and I. Capuzzo-Dolcetta. Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control: Foundations & Applications. Birkhiiuser Boston Inc., Boston, MA, 1997. With appendices by Maurizio Falcone and Pierpaolo Saravia.

[CIL] M. G. Crandall, H. Ishii, and P.-L. Lions. User's guide to viscosity solutions of second order partial differential

equations. Bull. Amer. Math. Soc. {N.S.), 27(1):1-67, 1992.

[GS] W. Gangbo and A. Swiech. Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes.

Cale. Var. Partial Differential Equations, 54(1):1183-1218, 2015.

[GHN] Y. Giga, N. Hamamuki, and A. Nakayasu. Eikonal equations in metric spaces. Trans. Amer. Math. Soc.,

367(1):49-66, 2015.

[LSZ] Q. Liu, N. Shanmugalingam, and X. Zhou. Equivalence of solutions of eikonal equation in metric spaces. J.

Differential Equations, 272 (2021), 979-1014.

[NS] R. T. Newcomb, II and J. Su. Eikonal equations with discontinuities. Differential Integral Equations, 8(8):19471960, 1995.

XIAODAN ZHOU, ANALYSIS ON METRIC SPACES UNIT, OKINAWA INSTITUTE OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY, OKINAWA

904-0495,

JAPAN,

...

参考文献をもっと見る

分野

大学

学位論文種類・取得年

言語

EIKONAL EQUATIONS ON METRIC SPACES (Women in Mathematics)

概要

この論文で使われている画像

関連論文

On Soliton Solutions of the Anti-Self-Dual Yang-Mills Equations from the Perspective of Integrable Systems

A Lie algebra-based approach to asymptotic symmetries in general relativity

Scattering theory for half-line Schrödinger operators: analytic and topological results

表紙・目次

The Ko-Valued Spectral Flow for Skew-Adjoint Fredholm Operators

参考文献

分野

大学

学位論文種類・取得年

言語

コピーが完了しました

URLをコピーしました

EIKONAL EQUATIONS ON METRIC SPACES (Women in Mathematics)

概要

この論文で使われている画像

関連論文

On Soliton Solutions of the Anti-Self-Dual Yang-Mills Equations from the Perspective of Integrable Systems

A Lie algebra-based approach to asymptotic symmetries in general relativity

Scattering theory for half-line Schrödinger operators: analytic and topological results

表紙・目次

The Ko-Valued Spectral Flow for Skew-Adjoint Fredholm Operators

参考文献