Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere

Masashi Misawa, Takayoshi Ogawa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold M into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion ∫0T ||∇u(τ)|| BMOr2dτ where BMOr is the space of bounded mean oscillations on M. A sharp version of the Sobolev inequality of the Brezis-Gallouet type is introduced on M. A monotonicity formula by the mean oscillation is established and applied for proving such a regularity criterion for weak solutions as above.

Original languageEnglish
Pages (from-to)391-415
Number of pages25
JournalCalculus of Variations and Partial Differential Equations
Volume33
Issue number4
DOIs
Publication statusPublished - 2008 Dec 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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