Abstract
We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem \({u_t = \Delta_{\infty}^{h} u}\) , where \({\Delta_{\infty}^{h}}\) is the h-homogeneous operator associated with the infinity-Laplacian, \({\Delta_{\infty}^{h} u = |Du|^{h-3} \langle D^{2}uDu, Du \rangle}\) , and h > 1. We also derive the asymptotic behaviour of u for the problem posed in the whole space, and for the Dirichlet problem posed in a bounded domain with zero boundary conditions.
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Communicated by O. Savin.
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Portilheiro, M., Vázquez, J.L. Degenerate homogeneous parabolic equations associated with the infinity-Laplacian. Calc. Var. 46, 705–724 (2013). https://doi.org/10.1007/s00526-012-0500-9
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DOI: https://doi.org/10.1007/s00526-012-0500-9