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A maximum principle for evolution Hamilton-Jacobi equations on Riemannian manifolds

Azagra Rueda, Daniel and Ferrera Cuesta, Juan and López-Mesas Colomina, Fernando (2006) A maximum principle for evolution Hamilton-Jacobi equations on Riemannian manifolds. Journal of Mathematical Analysis and Applications, 323 (1). pp. 473-480. ISSN 0022-247X

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Abstract

We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form u(t) + F(t, d(x)u) = 0, u(0, x) = u(0)(x), where u(0): M -> R is a bounded uniformly continuous function, M is a Riemannian manifold, and F: [0, infinity) x T*M -> R. This yields uniqueness of the viscosity solutions of such Hamilton-Jacobi equations.


Item Type:Article
Uncontrolled Keywords:Infinite dimensions; Nonsmooth analysis; Hamilton-Jacobi equations; viscosity solutions; Riemannian manifolds
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Differential equations
ID Code:14772
Deposited On:17 Apr 2012 11:50
Last Modified:06 Feb 2014 10:08

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