Lojasiewicz--Simon gradient inequalities for the harmonic map energy function

We apply our abstract gradient inequalities developed by the authors in arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity requirements on maps between closed, Riemannian manifolds. Our Lojasiewicz--Simon gradient inequalities for the harmonic map energy function generalize those of Kwon (2002), Liu and Yang (2010), Simon (1983, 1985), and Topping (1997).