Uniqueness of Values of Aronsson Operators and Running Costs in “tug-of-War” Games

Yu, Yifeng

doi:10.1016/j.anihpc.2008.11.001

Yu, Yifeng

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1299-1308.

MR 2542726 | Zbl 1176.35074

DOI : https://doi.org/10.1016/j.anihpc.2008.11.001

BibTeX
RIS

@article{AIHPC_2009__26_4_1299_0,
     author = {Yu, Yifeng},
     title = {Uniqueness of {Values} of {Aronsson} {Operators} and {Running} {Costs} in {{\textquotedblleft}tug-of-War{\textquotedblright}} {Games}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1299--1308},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.11.001},
     zbl = {1176.35074},
     mrnumber = {2542726},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.11.001/}
}

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
DA  - 2009///
SP  - 1299
EP  - 1308
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.11.001/
UR  - https://zbmath.org/?q=an%3A1176.35074
UR  - https://www.ams.org/mathscinet-getitem?mr=2542726
UR  - https://doi.org/10.1016/j.anihpc.2008.11.001
DO  - 10.1016/j.anihpc.2008.11.001
LA  - en
ID  - AIHPC_2009__26_4_1299_0
ER  -

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, Tome 26 (2009) no. 4, pp. 1299-1308. doi : 10.1016/j.anihpc.2008.11.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.11.001/

Bibliographie
Cité par

[1] Aronsson G., Minimization Problem for the Functional $\sup_{x} F (x, f (x), f^{'} (x))$ , Ark. Mat. 6 (1965) 33-53. | MR 196551 | Zbl 0156.12502

[2] Aronsson G., Minimization Problem for the Functional $\sup_{x} F (x, f (x), f^{'} (x))$ . II, Ark. Mat. 6 (1969) 409-431. | MR 203541 | Zbl 0156.12502

[3] Aronsson G., Extension of Functions Satisfying Lipschitz Conditions, Ark. Mat. 6 (1967) 551-561. | MR 217665 | Zbl 0158.05001

[4] Aronsson G., Minimization Problem for the Functional $\sup_{x} F (x, f (x), f^{'} (x))$ . III, Ark. Mat. 7 (1969) 509-512. | MR 240690 | Zbl 0181.11902

[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). | MR 2341994 | Zbl 1125.35019

[6] Barron E. N., Jensen R., Wang C., The Euler Equation and Absolute Minimizers of $L^{\infty}$ Functionals, Arch. Ration. Mech. Anal. 157 (4) (2001) 255-283. | MR 1831173 | Zbl 0979.49003

[7] Crandall M. G., An Efficient Derivation of the Arronson Equation, Arch. Ration. Mech. Anal. 167 (4) (2003) 271-279. | MR 1981858 | Zbl 1090.35067

[8] Crandall M. G., Evans L. C., Gariepy R., Optimal Lipschitz Extensions and the Infinity Laplacian, Cal. Var. Partial Differential Equations 13 (2) (2001) 123-139. | MR 1861094 | Zbl 0996.49019

[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. | MR 1118699 | Zbl 0755.35015

[10] Crandall M. G., Wang C., Yu Y., Derivation of Aronsson Equation for $C^{1}$ Hamiltonian, Trans. Amer. Math. Soc. 361 (2009) 103-124. | MR 2439400 | Zbl 1161.49020

[11] Evans L. C., Some Min-Max Methods for the Hamilton-Jacobi Equation, Indiana Univ. Math. J. 33 (1) (1984) 31-50. | MR 726105 | Zbl 0543.35012

[12] Jensen R., Uniqueness of Lipschitz Extensions: Minimizing the Sup Norm of the Gradient, Arch. Ration. Mech. Anal. 123 (1) (1993) 51-74. | MR 1218686 | Zbl 0789.35008

[13] Frankowska H., On the Single Valuedness of Hamilton-Jacobi Operators, Nonlinear Anal. 10 (12) (1986) 1477-1483. | MR 869555 | Zbl 0535.35010

[14] Gariepy R., Wang C., Yu Y., Generalized Cone Comparison, Aronsson Equation, and Absolute Minimizers, Comm. Partial Differential Equations 31 (7-9) (2006) 1027-1046. | MR 2254602

[15] Juutinen P., Minimization Problems for Lipschitz Functions Via Viscosity Solutions, Ann. Acad. Sci. Fenn. Math. Diss. 115 (1998). | MR 1632063 | Zbl 0902.35037

[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. | MR 2449057

[17] Yu Y., $L^{\infty}$ Variational Problems and the Aronsson Equations, Arch. Ration. Mech. Anal. 182 (1) (2006) 153-180. | MR 2247955 | Zbl 1130.49025

Cité par Sources :