On the Lojasiewicz-Simon gradient inequality on submanifolds

Abstract

We provide sufficient conditions for the Lojasiewicz-Simon gradient inequality to hold on a submanifold of a Banach space and discuss the optimality of our assumptions. Our result provides a tool to study asymptotic properties of quasilinear parabolic equations with (nonlinear) constraints.

arXiv comment32 pages. To appear in Journal of Functional Analysis. New version contains an abstract convergence result (Cor. 5.6), a new counterexample (Ex. 6.5) and minor corrections. 2 references added

References in corpus (2)

• The Łojasiewicz-Simon gradient inequality for open elastic curves
• Lojasiewicz-Simon gradient inequalities for analytic and Morse-Bott functions on Banach spaces

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