Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Petri Juutinen, Eero Saksman
2009 Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V  
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∈B r (x) u(y) and r → min y∈B r (x) u(y), respectively. (2000) : 35J60 (primary); 49L25, 35F25
more » ... ); 49L25, 35F25 (secondary). Mathematics Subject Classification
doi:10.2422/2036-2145.2007.1.01 fatcat:scexejeybnbgnf6li3bddbseeu