Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Petri Juutinen; Eero Saksman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

  • Volume: 6, Issue: 1, page 1-13
  • ISSN: 0391-173X

Abstract

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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 r ↦ max y ∈ B r ( x ) u ( y ) and r ↦ min y ∈ B r ( x ) u ( y ) , respectively.

How to cite

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Juutinen, Petri, and Saksman, Eero. "Hamilton-Jacobi flows and characterization of solutions of Aronsson equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.1 (2007): 1-13. <http://eudml.org/doc/272275>.

@article{Juutinen2007,
abstract = {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.},
author = {Juutinen, Petri, Saksman, Eero},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Scuola Normale Superiore, Pisa},
title = {Hamilton-Jacobi flows and characterization of solutions of Aronsson equations},
url = {http://eudml.org/doc/272275},
volume = {6},
year = {2007},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 1
SP - 1
EP - 13
AB - 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.
LA - eng
UR - http://eudml.org/doc/272275
ER -

References

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