Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian

References

• Chen YG, Giga Y, Goto S. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differ Geom. 1991;33:749–786.
   Web of Science ®Google Scholar
• Crandall M, Ishii H, Lions PL. User’s guide to viscosity solutions of second order partial differential equations. Bull Am Math Soc. 1992;27:1–67.
   Web of Science ®Google Scholar
• Attouchi A, Parviainen M. Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian. Commun Contemp Math. 2016. to appear in preprint arXiv 1610.04987.
   Web of Science ®Google Scholar
• Attouchi A, Parviainen M, Ruosteenoja E. C1, regularity for the normalized p-Poisson problem. J Math Pures Appl. 2017;108(9):553–591.
   Google Scholar
• Banerjee A, Garofalo N. Gradient bounds and monotonicity of the energy for some nonlinear singular diffusion equations. Indiana Univ Math J. 2013;62:699–736.
   Web of Science ®Google Scholar
• Banerjee A, Garofalo N. On the Dirichlet boundary value problem for the normalized p-Laplacian evolution. Commun Pure Appl Anal. 2015;14:1–21.
   Web of Science ®Google Scholar
• Does K. An evolution equation involving the normalized p-Laplacian. Commun Pure Appl Anal. 2011;10:361–396.
   Web of Science ®Google Scholar
• Juutinen P, Kawohl B. On the evolution governed by the infinity Laplacian. Math Ann. 2006;335:819–851.
   Web of Science ®Google Scholar
• Kawohl B, Horák J. On the geometry of the p-Laplacian operator. Discrecte Contin. Dyn Syst Ser S. 2017;10:799–813.
   Web of Science ®Google Scholar
• Kawohl B, Krömer S, Kurtz J. Radial eigenfunctions for the game-theoretic p-Laplacian on a ball. Differ Integral Equ. 2014;27:659–670.
   Web of Science ®Google Scholar
• Manfredi JJ, Parviainen M, Rossi JD. An asymptotic mean value characterization for a class of nonlinear parabolic equations related to tug-of-war games. SIAM J Math Anal. 2010;42:2058–2081.
   Web of Science ®Google Scholar
• Manfredi JJ, Parviainen M, Rossi JD. An asymptotic mean value characterization for p-harmonic functions. Proc Am Math Soc. 2010;138:881–889.
   Web of Science ®Google Scholar
• Peres Y, Sheffield S. Tug-of-war with noise: a game-theoretic view of the p-Laplacian. Duke Math J. 2008;145:91–120.
   Web of Science ®Google Scholar
• Peres Y, Schramm O, Sheffield S, Wilson DB. Tug-of-war and the infinity Laplacian. J Am Math Soc. 2009;22:167–210.
   Web of Science ®Google Scholar
• Baravdish G, Svensson O, Åström F. On backward p-parabolic equations for image enhancement. Numer Funct Anal Optim. 2015;36:147–168.
   Web of Science ®Google Scholar
• Freidlin MI, Wentzell AD. Random perturbations of dynamical systems. New York (NY): Springer-Verlag; 1984.
   Google Scholar
• Varadhan SRS. On the behavior of the fundamental solution of the heat equation with variable coefficients. Commun Pure Appl Math. 1967;20:431–455.
   Web of Science ®Google Scholar
• Evans LC, Ishii H. A PDE approach to some asymptotics problem concerning random differential equations with small noise intensities. Ann Inst Henri Poincaré Anal Nonlinear. 1985;2:1–20.
   Web of Science ®Google Scholar
• Magnanini R, Sakaguchi S. Matzoh ball soup: heat conductors with a stationary isothermic surface. Ann Math. 2002;156:931–946.
   Web of Science ®Google Scholar
• Magnanini R, Sakaguchi S. Stationary isothermic surfaces for unbounded domains. Indiana Univ Math J. 2007;56:2723–2738.
   Web of Science ®Google Scholar
• Magnanini R, Sakaguchi S. Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space. J Differ Equ. 2010;248:1112–1119.
   Web of Science ®Google Scholar
• Magnanini R, Sakaguchi S. Matzoh ball soup revisited: the boundary regularity issue. Math Meth Appl Sci. 2013;36:2023–2032.
   Web of Science ®Google Scholar
• Magnanini R, Marini M. The Matzoh Ball Soup problem: a complete characterization. Nonlinear Anal. 2016;131:170–181.
   Web of Science ®Google Scholar
• Magnanini R, Sakaguchi S. Interaction between degenerate diffusion and shape of domain. Proc R Soc Edinburgh. 2007;137A:373–388.
   Google Scholar
• Magnanini R, Sakaguchi S. Nonlinear diffusion with a bounded stationary level surface. Ann Inst Henri Poincaré Anal Nonlinear. 2010;27:937–952.
   Web of Science ®Google Scholar
• Magnanini R, Sakaguchi S. Interaction between nonlinear diffusion and geometry of domain. J Differ Equ. 2012;252:236–257.
   Web of Science ®Google Scholar
• Sakaguchi S. Interaction between fast diffusion and geometry of domain. Kodai Math J. 2014;37:680–701.
   Web of Science ®Google Scholar
• Magnanini R, Peralta-Salas D, Sakaguchi S. Stationary isothermic surfaces in Euclidean 3-space. Math Ann. 2016;364:97–124.
   Web of Science ®Google Scholar
• Magnanini R, Prajapat J, Sakaguchi S. Stationary isothermic surfaces and uniformly dense domains. Trans Am Math Soc. 2006;358:4821–4841.
   Web of Science ®Google Scholar
• Sakaguchi S. Two-phase heat conductors with a stationary isothermic surface. Rend Ist Mat Univ Trieste. 2016;48:167–187.
   Google Scholar
• Sakaguchi S. Two-phase heat conductors with a stationary isothermic surface and their related elliptic overdetermined problems. 2017. preprint, arXiv:1705.10628v1.
   Google Scholar
• Cavallina L, Magnanini R, Sakaguchi S. Two-phase heat conductors with a surface of the constant flow property. 2018. submitted, preprint, arXiv:1801.01352v1.
   Google Scholar
• Ishiwata M, Magnanini R, Wadade H. A natural approach to the asymptotic mean value property for the p-Laplacian. Calc Var Part Differ Equ. 2017;56(4):22 pp. Art. 97.
   Web of Science ®Google Scholar
• Berti D, Magnanini R. Short-time behaviour for game-theoretic p-caloric functions. J Math Pures Appl. 2017. to appear in preprint arXiv:1709.10005.
   Web of Science ®Google Scholar
• Alexandrov AD. Uniqueness theorems for surfaces in the large V. Vestnik Leningrad Univ. 1958;13(19):5–8; Am Math Soc Transl Ser. 2, 1962;21:412--416.
   Google Scholar
• Ciraolo G, Magnanini R, Sakaguchi S. Symmetry of minimizers with a level surface parallel to the boundary. J Eur Math Soc. 2015;17:2789–2804.
   Web of Science ®Google Scholar
• Abramowitz M, Stegun IA. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Nat Bureau Standards Appl Math Ser. 1972;55. Washington (DC). 10th printing with corrections.
   Google Scholar
• Sato M-H. Comparison principle for singular degenerate elliptic equations on unbounded domains. Proc Jpn Acad Ser A Math Sci. 1990;66:252–256.
   Google Scholar
• Lieb E, Loss M. Analysis. Providence (RI): American Mathematical Society; 2001. second version.
   Google Scholar