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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 and , respectively.
@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},
pages = {1--13},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {1},
year = {2007},
mrnumber = {2341511},
zbl = {1150.35017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_1_0/}
}
TY - JOUR AU - Juutinen, Petri AU - Saksman, Eero TI - Hamilton-Jacobi flows and characterization of solutions of Aronsson equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 1 EP - 13 VL - 6 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_1_0/ LA - en ID - ASNSP_2007_5_6_1_1_0 ER -
%0 Journal Article %A Juutinen, Petri %A Saksman, Eero %T Hamilton-Jacobi flows and characterization of solutions of Aronsson equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 1-13 %V 6 %N 1 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_1_0/ %G en %F 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, Série 5, Tome 6 (2007) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_1_0/