An improved uniqueness result for the harmonic map flow in two dimensions

DOI10.1007/s00526-008-0164-7zbMath1157.58004OpenAlexW2148387785MaRDI QIDQ956656

Melanie Rupflin

Publication date: 25 November 2008

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/3960

zbMATH Keywords

energy functionaluniqueness theoremweak heat flow for harmonic maps

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Harmonic maps, etc. (58E20) Variational inequalities (global problems) in infinite-dimensional spaces (58E35)

Related Items (14)

Regularity at the free boundary for Dirac-harmonic maps from surfaces ⋮ Global weak solutions of the Teichmüller harmonic map flow into general targets ⋮ Regularity at the free boundary for approximate H-surfaces in Riemannian manifolds ⋮ The qualitative behavior at the free boundary for approximate harmonic maps from surfaces ⋮ Selfsimilar expanders of the harmonic map flow ⋮ Vortex dynamics in the presence of excess energy for the Landau-Lifshitz-Gilbert equation ⋮ The Lamm-Rivière system. I: \(L^p\) regularity theory ⋮ Uniqueness of weak solutions for the normalised Ricci flow in two dimensions ⋮ Flowing maps to minimal surfaces: existence and uniqueness of solutions ⋮ Uniqueness for the Heat Flow for Extrinsic Polyharmonic Maps in the Critical Dimension ⋮ Decay estimates for Rivière’s equation, with applications to regularity and compactness ⋮ An 𝐿^{𝑝} regularity theory for harmonic maps ⋮ Regularity for Dirac-harmonic maps into certain pseudo-Riemannian manifolds ⋮ \(L^p\)-regularity for fourth order elliptic systems with antisymmetric potentials in higher dimensions

Cites Work

• Unnamed Item
• On the evolution of harmonic mappings of Riemannian surfaces
• Uniqueness for the harmonic map flow in two dimensions
• Nonuniqueness for the heat flow of harmonic maps on the disk
• Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps
• Partial regularity for harmonic maps and related problems

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