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Currently displaying 1 – 2 of 2

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Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Petri Juutinen; Eero Saksman — 2007

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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 $r \mapsto {max}_{y \in B_{r} (x)} u (y)$ and $r \mapsto {min}_{y \in B_{r} (x)} u (y)$ , respectively.

Absolutely minimizing Lipschitz extensions on a metric space.

Juutinen, Petri — 2002

Annales Academiae Scientiarum Fennicae. Mathematica

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