Bubbling analysis near the Dirichlet boundary for approximate harmonic maps from surfaces (Q2322321)

In this paper, the authors study a Dirichlet boundary condition from a compact Riemann surface with smooth boundary to a general compact Riemannian manifold, with uniformly bounded energy and with uniformly \(L^2\)-bounded tension field. The main results include: (1) Showing that the energy identity and the no-neck property hold during a blow-up process near the Dirichlet boundary. (2) Applying these results to the two-dimensional harmonic map flow with Dirichlet boundary and prove the energy identity at finite and infinite singular time. Finally, they check the no-neck property holds at infinite time.