Positively homogeneous functions and the Łojasiewicz gradient inequality
Volume 87 / 2005
Annales Polonici Mathematici 87 (2005), 165-174
MSC: 26B35, 26E05, 34A26, 34D05.
DOI: 10.4064/ap87-0-13
Abstract
It is quite natural to conjecture that a positively homogeneous function with degree $d\geq 2$ on ${{\mathbb R}}^N$ satisfies the Łojasiewicz gradient inequality with exponent $\theta = 1/d $ without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for $ N= 2$.
