Addendum to "Relative Newtonian Potentials of Radial Functions and Asymptotics in Nonlinear Diffusion"

@article{Chung2013AddendumT,
  title={Addendum to "Relative Newtonian Potentials of Radial Functions and Asymptotics in Nonlinear Diffusion"},
  author={Jaywan Chung and Yong Jung Kim},
  journal={SIAM J. Math. Anal.},
  year={2013},
  volume={45},
  pages={728-731}
}
Theorem 9.7 of Lieb and Loss [Analysis, AMS, Providence, RI, 2000] is an extended version of Newton's theorem and was cited in the authors' previously published paper [SIAM J. Math. Anal., 43 (2011), pp. 1975--1994]. However, the statement of this theorem is incorrect for dimensions $d\le2$. A couple of comments and, in particular, Figure 1 in the authors' paper [SIAM J. Math.\Anal., 43 (2011), pp. 1975--1994] are based on this theorem and are incorrect because of this reason. In this note we… 

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Relative Newtonian Potentials of Radial Functions and Asymptotics in Nonlinear Diffusion
TLDR
Newton's theorem is revised in terms of relative potentials, which is a simpler argument that works for all dimensions $d\ge1$ and is used to obtain the L^1-convergence order for radially symmetric solutions to the porous medium and fast diffusion equations.
Analysis
TLDR
The parser, especially its mapping rule interpreter, used in KBMT-89 is described, characterized by its ability to produce semantic and syntactic structures of a parse simultaneously and therefore more efficiently than other kinds of analyzers.
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Analysis, volume 14 of Graduate Studies in Mathematics
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