[1] Manfredi J J, Parviainen M, Rossi J D. An asymptotic mean value characterization of p-harmonic functions. Proc Amer Math Soc, 2010, 138: 881-889
[2] Giorgi T, Smits R. Mean value property for p-harmonic functions. Proc Amer Math Soc, 2012, 140(7): 2453-2463
[3] Kawohl B, Manfredi J, Parviainen M. Solutions of nonlinear PDEs in the sense of averages. J Math Pures Appl, 2012, 97: 173-188
[4] Manfredi J J, Parviainen M, Rossi J D. An asymptotic mean value characterization for a class of nonlinear parabolic equations related to tug-of-war games. SIAM J Math Anal, 2010, 42(5): 2058-2081
[5] Barron E N, Evans L C, Jensen R. The infinity Laplacian, Aronsson's equation and their generalizations. Trans Amer Math Soc, 2008, 360: 77-101
[6] Le Gruyer E, Archer J C. Harmonious extensions. SIAM J Math Anal, 1998, 29: 279-292
[7] Le Gruyer E. On absolutely minimizing Lipschitz extensions and PDE Δ∞u = 0. Nonlinear Differential Equations Appl, 2007, 14: 29-55
[8] Peres Y, Schramm O, Sheffield S, Wilson D. Tug of war and the infinity Laplacian. J Amer Math Soc, 2009, 22(1): 167-210
[9] Lu G, Wang P. Infinity Laplace equation with non-trivial right-hand side. Electr J Diff Equ, 2010, 77: 1-12
[10] Lu G, Wang P. Inhomogeneous infinity Laplace equation. Advances in Mathematics, 2008, 217(4): 1838- 1868
[11] Lu G, Wang P. A PDE perspective of the normalized infinity Laplacian. Communications in Partial Dif- ferential Equations, 2008, 33: 1788-1817
[12] Lu G, Wang P. A uniqueness theorem for degenerate elliptic equations//Lecture Notes of Seminario Inter- disciplinare di Matematica, Conference on Geometric Methods in PDE's. On the Occasion of 65th Birthday of Ermanno Lanconelli Bologna, 2008: 207-222
[13] Liu F, Yang X. Solutions to an inhomogeneous equation involving infinity-Laplacian. Nonlinear Analysis: Theory, Methods and Applications, 2012, 75(14): 5693-5701
[14] Peres Y, Sheffield S. Tug-of-war with noise: A game theoretic view of the p-Laplacian. Duke Math J, 2008, 145(1): 91-120
[15] Caselles V, Morel J M, Sbert C. An axiomatic approach to image interpolation. IEEE Trans Image Process, 1998, 7(3): 376-386
[16] Portilheiro M, Vázquez J L. Degenerate homogeneous parabolic equations associated with the infinity- Laplacian. Calc Var and Partial Differential Equations, 2012, 31: 457-471
[17] Portilheiro M, Vázquez J L. A porous medium equation involving the infinity-Laplacian. Viscosity solutions and asymptotic behaviour. Communications in Partial Differential Equations, 2012, 37: 753-793
[18] Crandall M G, Wang P. Another way to say caloric. J Evol Equ, 2004, 3: 653-672
[19] Akagi G, Suzuki K. On a certain degenerate parabolic equation associated with the infinity-Laplacian. Discrete and Continuous Dynamical Systems (Supplement), 2007: 18-27
[20] Akagi G, Suzuki K. Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian. Calc Var and Partial Differential Equations, 2008, 31: 457-471
[21] Akagi G, Juutinen P, Kajikiya R. Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian. Math Ann, 2009, 343: 921-953
[22] Laurencot P, Stinner C. Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions. Communications in Partial Differential Equations, 2010, 36(3): 532-546
[23] Does K. An evolution equation involving the normalized p-Laplacian. Comm Pure Appl Anal, 2011, 10: 361-396; University of Cologne: Dissertation under the same title, 2009
[24] Kawohl B. Variations on the p-Laplacian//Nonlinear Elliptic Partial Differential Equations. Contemporary Mathematics, 2011, 540: 35-46
[25] Manfredi J J, Parviainen M, Rossi J D. On the definition and properties of p-harmonious functions. Ann Sc Norm Super Pisa CI Sci, 2012, 11(2): 215-241
[26] Manfredi J J, Parviainen M, Rossi J D. Dynamic programming principle for tug-of-war games with noise. ESAIM Control Optim Cal Var, 2012, 18(1): 81-90
[27] Juutinen P, Kawohl B. On the evolution governed by the infinity Laplacian. Math Ann, 2006, 335: 819-851
[28] Evans L C, Spruck J. Motion of level sets by mean curvature I. J Differential Geom, 1991, 33: 635-681
[29] Crandall M G, Ishii H, Lions P L. User's guide to viscosity solutions of second-order partial differential equations. Bull A M S, 1992, 27: 1-67
[30] Ohnuma S, Sato K. Singular degenerate parabolic equations with applications to the p-Laplace diffusion equation. Communications in Partial Differential Equations, 1997, 22: 381-411
[31] Falcome M, Finzi Vita S, Giorgi T, Smits R. A semi-Lagrangian scheme for the game p-Laplacian via p-averaging. Applied Numerical Mathematics, 2013, 73: 63-80
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