Addendum to “Relative Newtonian Potentials of Radial Functions and Asymptotics in Nonlinear Diffusion''
Jaywan Chung, Yong Jung Kim · SIAM Journal on Mathematical Analysis · 2013
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 show another extended version of Newton's theorem and provide a corrected figure. This correction makes the arguments in the original paper more general.