Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games

Yifeng Yu

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 4, page 1299-1308
  • ISSN: 0294-1449

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Yu, Yifeng. "Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games." Annales de l'I.H.P. Analyse non linéaire 26.4 (2009): 1299-1308. <http://eudml.org/doc/78891>.

@article{Yu2009,
author = {Yu, Yifeng},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Aronsson operators; infinity Laplacian operator; ``tug-of-war'' games},
language = {eng},
number = {4},
pages = {1299-1308},
publisher = {Elsevier},
title = {Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games},
url = {http://eudml.org/doc/78891},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Yu, Yifeng
TI - Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 4
SP - 1299
EP - 1308
LA - eng
KW - Aronsson operators; infinity Laplacian operator; ``tug-of-war'' games
UR - http://eudml.org/doc/78891
ER -

References

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  2. [2] Aronsson G., Minimization problem for the functional sup x F ( x , f ( x ) , f ' ( x . II, Ark. Mat.6 (1969) 409-431. Zbl0156.12502MR203541
  3. [3] Aronsson G., Extension of functions satisfying Lipschitz conditions, Ark. Mat.6 (1967) 551-561. Zbl0158.05001MR217665
  4. [4] Aronsson G., Minimization problem for the functional sup x F ( x , f ( x ) , f ' ( x . III, Ark. Mat.7 (1969) 509-512. Zbl0181.11902MR240690
  5. [5] Barron E.N., Evans L.C., Jensen R., The infinity Laplacian, Aronsson's equation and their generalizations, Trans. Amer. Math. Soc.360 (1) (2008) 77-101, (electronic). Zbl1125.35019MR2341994
  6. [6] Barron E.N., Jensen R., Wang C., The Euler equation and absolute minimizers of L functionals, Arch. Ration. Mech. Anal.157 (4) (2001) 255-283. Zbl0979.49003MR1831173
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  8. [8] Crandall M.G., Evans L.C., Gariepy R., Optimal Lipschitz extensions and the infinity Laplacian, Cal. Var. Partial Differential Equations13 (2) (2001) 123-139. Zbl0996.49019MR1861094
  9. [9] Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc.27 (1992) 1-67. Zbl0755.35015MR1118699
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  11. [11] Evans L.C., Some min-max methods for the Hamilton–Jacobi equation, Indiana Univ. Math. J.33 (1) (1984) 31-50. Zbl0543.35012MR726105
  12. [12] Jensen R., Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient, Arch. Ration. Mech. Anal.123 (1) (1993) 51-74. Zbl0789.35008MR1218686
  13. [13] Frankowska H., On the single valuedness of Hamilton–Jacobi operators, Nonlinear Anal.10 (12) (1986) 1477-1483. Zbl0535.35010MR869555
  14. [14] Gariepy R., Wang C., Yu Y., Generalized cone comparison, Aronsson equation, and absolute minimizers, Comm. Partial Differential Equations31 (7–9) (2006) 1027-1046. Zbl1237.35052MR2254602
  15. [15] Juutinen P., Minimization problems for Lipschitz functions via viscosity solutions, Ann. Acad. Sci. Fenn. Math. Diss.115 (1998). Zbl0902.35037MR1632063
  16. [16] Peres Y., Schramm O., Sheffield S., Wilson D.B., Tug-of-war and the infinity Laplacian, J. Amer. Math. Soc. Math.22 (2009) 167-210. Zbl1206.91002MR2449057
  17. [17] Yu Y., L variational problems and the Aronsson equations, Arch. Ration. Mech. Anal.182 (1) (2006) 153-180. Zbl1130.49025MR2247955

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