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

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 ≤ 2. 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.