Uniform small energy regularity for fractional geometric problems

Abstract

We prove small energy regularity for a parabolic boundary reaction Ginzburg-Landau problem in the full range s∈ (0,1), answering a question posed by Hyder, Segatti, Sire and Wang. We also obtain a similar small energy regularity result for fractional harmonic maps to spheres. Both results are uniform as s 1.

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