A differential equation related to the $l^p$-norms

Jacek Bojarski, Tomasz Małolepszy, and Janusz Matkowski. "A differential equation related to the $l^{p}$-norms." Annales Polonici Mathematici 101.3 (2011): 251-265. <http://eudml.org/doc/280319>.

@article{JacekBojarski2011,
abstract = {Let p ∈ (1,∞). The question of existence of a curve in ℝ₊² starting at (0,0) and such that at every point (x,y) of this curve, the $l^\{p\}$-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.},
author = {Jacek Bojarski, Tomasz Małolepszy, Janusz Matkowski},
journal = {Annales Polonici Mathematici},
keywords = {Euclidean norm in ; -norm; curve; inner product; conjugate norm},
language = {eng},
number = {3},
pages = {251-265},
title = {A differential equation related to the $l^\{p\}$-norms},
url = {http://eudml.org/doc/280319},
volume = {101},
year = {2011},
}

TY - JOUR
AU - Jacek Bojarski
AU - Tomasz Małolepszy
AU - Janusz Matkowski
TI - A differential equation related to the $l^{p}$-norms
JO - Annales Polonici Mathematici
PY - 2011
VL - 101
IS - 3
SP - 251
EP - 265
AB - Let p ∈ (1,∞). The question of existence of a curve in ℝ₊² starting at (0,0) and such that at every point (x,y) of this curve, the $l^{p}$-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.
LA - eng
KW - Euclidean norm in ; -norm; curve; inner product; conjugate norm
UR - http://eudml.org/doc/280319
ER -