A differential equation related to the $\mathbf{l}^{p}$-norms
Annales Polonici Mathematici, Tome 101 (2011) no. 3, pp. 251-265
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $p\in (1,\infty )$. The question of existence of a curve in $\mathbb{R}%
_{+}^{2}$ starting at $(0,0)$ and such that at every point $(x,y)$ of this
curve, the $\mathbf{l}^{p}$-distance of the points $(x,y)$ and $(0,0)$ is
equal to the Euclidean length of the arc of this curve between these
points is considered. This problem reduces to a nonlinear differential
equation. The existence and uniqueness of solutions is proved and
nonelementary explicit solutions are given.
Keywords:
infty question existence curve mathbb starting every point curve mathbf distance points equal euclidean length arc curve between these points considered problem reduces nonlinear differential equation existence uniqueness solutions proved nonelementary explicit solutions given
Affiliations des auteurs :
Jacek Bojarski 1 ; Tomasz Małolepszy 1 ; Janusz Matkowski 2
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title = {A differential equation related to the $\mathbf{l}^{p}$-norms},
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Jacek Bojarski; Tomasz Małolepszy; Janusz Matkowski. A differential equation related to the $\mathbf{l}^{p}$-norms. Annales Polonici Mathematici, Tome 101 (2011) no. 3, pp. 251-265. doi: 10.4064/ap101-3-5
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