English

On the Lojasiewicz-Simon gradient inequality on submanifolds

Functional Analysis 2020-07-27 v2 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.1907.09292,
  title  = {On the Lojasiewicz-Simon gradient inequality on submanifolds},
  author = {Fabian Rupp},
  journal= {arXiv preprint arXiv:1907.09292},
  year   = {2020}
}

Comments

32 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

R2 v1 2026-06-23T10:27:05.766Z