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MiS Preprint
38/2016

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

Jürgen Jost, Lei Liu and Miaomiao Zhu

Abstract

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:
Jun 29, 2016
Published:
Jun 29, 2016
MSC Codes:
53C43, 58E20
Keywords:
harmonic map, heat flow, Dirichlet boundary, blow-up, energy identity, no neck

Related publications

inJournal
2019 Repository Open Access
Jürgen Jost, Lei Liu and Miaomiao Zhu

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

In: Communications in analysis and geometry, 27 (2019) 3, pp. 639-669