Blow-up of Solutions to a p-Laplace Equation
نویسندگان
چکیده
Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field E blows up in the L∞-norm as δ, the distance between the conductors, tends to zero. We give here a concise rigorous justification of the rate of this blow-up in terms of δ. If the current-electric field relation is linear, see similar results obtained earlier in [E. S. Bao, Y. Y. Li, and B. Yin, Arch. Ration. Mech. Anal., 193 (2009), pp. 195–226; H. Kang, M. Lim, and K. H. Yun, preprint, http://arxiv.org/abs/1105.4328v1, 2011; M. Lim and K. Yun, Comm. Partial Differential Equations, 34 (2009), pp. 1287–1315; K. Yun, SIAM J. Appl. Math., 67 (2007), pp. 714–730; K. Yun, J. Math. Anal. Appl., 350 (2009), pp. 306–312].
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ورودعنوان ژورنال:
- Multiscale Modeling & Simulation
دوره 10 شماره
صفحات -
تاریخ انتشار 2012