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J. Math. Anal. Appl. 323 (2006) 473480 www.elsevier.com/locate/jmaa
 

Summary: J. Math. Anal. Appl. 323 (2006) 473­480
www.elsevier.com/locate/jmaa
A maximum principle for evolution
Hamilton­Jacobi equations on Riemannian manifolds
Daniel Azagra ,1
, Juan Ferrera, Fernando López-Mesas
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Received 14 June 2005
Available online 23 November 2005
Submitted by H. Frankowska
Abstract
We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form
ut + F(t,dxu) = 0, u(0,x) = u0(x), where u0 :M R is a bounded uniformly continuous function, M is
a Riemannian manifold, and F :[0,) × T M R. This yields uniqueness of the viscosity solutions of
such Hamilton­Jacobi equations.
© 2005 Elsevier Inc. All rights reserved.
Keywords: Hamilton­Jacobi equations; Viscosity solutions; Riemannian manifolds
First order Hamilton­Jacobi equations are partial differential equations of the form
F x,u(x),du(x) = 0
in the stationary case, and of the form,

  

Source: Azagra Rueda, Daniel - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

 

Collections: Mathematics