Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary
Ali Hyder, Antonio Segatti, Yannick Sire, Changyou Wang
Abstract
We introduce a heat flow associated to half-harmonic maps, which have been introduced by Da Lio and Rivière. Those maps exhibit integrability by compensation in one space dimension and are related to harmonic maps with free boundary. We consider a new flow associated to these harmonic maps with free boundary which is actually motivated by a rather unusual heat flow for half-harmonic maps. We construct then weak solutions and prove their partial regularity in space and time via a Ginzburg-Landau approximation. The present paper complements the study initiated by Struwe and Chen-Lin.
Topics & Concepts
Harmonic mapMathematicsBoundary (topology)HarmonicFlow (mathematics)Heat flowMathematical analysisDimension (graph theory)Harmonic measureSpace (punctuation)Pure mathematicsGeometryHarmonic functionThermalPhysicsComputer scienceThermodynamicsQuantum mechanicsOperating systemGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in Engineering