Publication: Uniqueness of the boundary behavior for large solutions to a
degenerate elliptic equation involving the ∞–Laplacian
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2003
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Springer
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Abstract
In this note we estimate the maximal growth rate at the boundary of viscosity solutions to −∆∞u + λ|u| m−1 u = f in Ω (λ > 0, m > 3).In fact, we prove that there is a unique explosive rate on the boundary for large solutions. A version of Liouville Theorem is also obtained when Ω = R N
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Aronsson, G., Crandall, M. G. and Juutinena, P. A tour of the theory of absolutely minimizing functions, preprint.
Bhattacharya, T.(2001). An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions, Electron. J. Differential Equations, 2001, No. 44, 1–8.
Crandall, M. G., Ishii, H. and Lions, P.-L. (1992). User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27, 1–42.
Crandall, M. C. and Zhang, J. (2003). Another way to say harmonic, Trans. Amer. Math. Soc., 355, 241–263.
Díaz, G. A state constraints problem governed by the ∞–Laplacian, in ellaboration.
Díaz, G. and Díaz, J. I. Large solutions to some degenerate elliptic equations involving the ∞–Laplacian case, to appear.
Díaz, G. and Letelier, R. (1993). Explosive solutions of quasilinear elliptic equations: existence and uniqueness, Nonlinear Analysis. TMA., 20, No.2, 97–125.
Gilbarg, D. and N. S. Trudinger, N. S. (1998). Elliptic Partial Differential Equation of Second Order, Springer Verlag, New York.
Lindqvist, P. and Manfredi, J. J. (1995). The Harnack inequality for ∞-harmonic functions, Electron. J. Differential Equations, 1995, No. 4, 1–5.