Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Juutinen, Petri; Saksman, Eero

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 1, pp. 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 $r\mapsto {max}_{y\in B_r\left(x\right)}u\left(y\right)$ and $r\mapsto {min}_{y\in B_r\left(x\right)}u\left(y\right)$, respectively.

Classification : 35J60, 49L25, 35F25

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