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2015 Extremal Viscosity Solutions of Almost Periodic Hamilton-Jacobi Equations
Marino Belloni, Silvana Marchi
Commun. Math. Anal. 18(2): 86-105 (2015).


This paper deals with viscosity solutions of Hamilton-Jacobi equations in which the Hamiltonian $H$ is weakly monotone with respect to the zero order term: this leads to non-uniqueness of solutions, even in the class of periodic or almost periodic (briefly a.p.) functions. The lack of uniqueness of a.p. solutions leads to introduce the notion of minimal (maximal) a.p. solution and to study its properties. The classes of asymptotically almost periodic (briefly a.a.p.) and pseudo almost periodic (briefly p.a.p.) functions are also considered.


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Marino Belloni. Silvana Marchi. "Extremal Viscosity Solutions of Almost Periodic Hamilton-Jacobi Equations." Commun. Math. Anal. 18 (2) 86 - 105, 2015.


Published: 2015
First available in Project Euclid: 30 October 2015

zbMATH: 1327.35007
MathSciNet: MR3418907

Primary: 35B15 , 35D40 , 35F21

Keywords: almost periodic solutions , Asymptotically almost periodic solutions , Hamilton-Jacobi equations , Pseudo almost periodic solutions , viscosity solutions

Rights: Copyright © 2015 Mathematical Research Publishers

Vol.18 • No. 2 • 2015
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