Some applications of the Łojasiewicz gradient inequality
Alain Haraux - UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France (email)
Abstract: In the present survey paper, basic convergence results for gradient-like systems relying on the Łojasiewicz gradient inequality are recalled in a self-contained way. A uniform version of the gradient inequality is used to get directly convergence and the rate of convergence in one step and a new technical trick, consisting in the evaluation of the integral of the velocity norm from $t$ to $2t$ is introduced. A short idea of the state of the art without technical details is also given.
Keywords: Łojasiewicz inequality, convergence, equilibrium solutions, rate of
Received: October 2010; Revised: November 2010; Published: April 2012.
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