Dirichlet problems for heat flows of harmonic maps in higher dimensions (Q803608)

In this note a monotonicity inequality and an \(\epsilon\)-regularity theorem for the Dirichlet problems of heat flows of harmonic maps are established. Then, one can prove that the sequence of the global regular solutions to the Dirichlet problem of heat flow of harmonic maps weakly converges to a global weak solution to this problem. Moreover, the partial regularity of this solution up to the boundary is investigated.