Positively homogeneous functions and the Łojasiewicz gradient inequality

Volume 87 / 2005

Alain Haraux Annales Polonici Mathematici 87 (2005), 165-174 MSC: 26B35, 26E05, 34A26, 34D05. DOI: 10.4064/ap87-0-13


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$.


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

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