Positively homogeneous functions and the Łojasiewicz gradient inequality

• Autorzy: Alain Haraux
• Języki publikacji: EN

Abstrakty

EN

It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on $ℝ^N$ satisfies the Łojasiewicz gradient inequality with exponent θ = 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.

Kategorie tematyczne

• 26E05: Real-analytic functions
• 26B35: Special properties of functions of several variables, H\"older conditions, etc.
• 34A26: Geometric methods in differential equations
• 34D05: Asymptotic properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 87
• Numer: 1
• Strony: 165-174

Daty

wydano

2005

Twórcy

autor

Alain Haraux

• Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/ap87-0-13