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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Bubbling analysis near the Dirichlet boundary for approximate harmonic maps from surfaces
Jürgen Jost, Lei Liu and Miaomiao ZhuAbstract
For a sequence of maps with 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 L2-bounded tension field, we show that the energy identity and the no neck property hold during a blow-up process near the Dirichlet boundary. We apply these results to the two dimensional harmonic map flow with Dirichlet boundary and prove the energy identity at finite and infinite singular time. Also, the no neck property holds at infinite time.
- Received:
- 29.06.16
- Published:
- 29.06.16
- MSC Codes:
- 53C43, 58E20
- Keywords:
- harmonic map, heat flow, Dirichlet boundary, blow-up, energy identity, no neck