Hamilton-Jacobi flows and characterization of solutions of Aronsson equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, p. 1-13

In this note, we verify the conjecture of Barron, Evans and Jensen [3] regarding the characterization of viscosity solutions of general Aronsson equations in terms of the properties of associated forward and backwards Hamilton-Jacobi flows. A special case of this result is analogous to the characterization of infinity harmonic functions in terms of convexity and concavity of the functions $r↦{max}_{y\in {B}_{r}\left(x\right)}u\left(y\right)$ and $r↦{min}_{y\in {B}_{r}\left(x\right)}u\left(y\right)$, respectively.

Classification:  35J60,  49L25,  35F25
@article{ASNSP_2007_5_6_1_1_0,
author = {Juutinen, Petri and Saksman, Eero},
title = {Hamilton-Jacobi flows and characterization of solutions of Aronsson equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {1},
year = {2007},
pages = {1-13},
zbl = {1150.35017},
mrnumber = {2341511},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2007_5_6_1_1_0}
}

Juutinen, Petri; Saksman, Eero. Hamilton-Jacobi flows and characterization of solutions of Aronsson equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, pp. 1-13. http://www.numdam.org/item/ASNSP_2007_5_6_1_1_0/

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