Interior estimates of harmonic heat flow.

Motivated by Giaquinta and Hildebrandt's regularity result for harmonic mappings [M. Giaquinta and S. Hildebrandt, A priori estimates for harmonic mappings, J. Reine Angew. Math. 1982(336) (1982) 124–164, Theorems 3 and 4], we show a C α , α 2 -regularity result of the harmonic flow between two Riemannian manifolds when the image is in a regular geodesic ball. The proof is based on De Giorgi–Moser's iteration and Schauder estimate. [ABSTRACT FROM AUTHOR]