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

2019/03/05 by Paul M. N. Feehan, Feehan, Paul M. N., Manousos Maridakis +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.01953

openalex publication_date 2019/03/05 · openalex created_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

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).

Citations

• Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow

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