2008年12月

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

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
• Masashi Misawa
• ,
• Takayoshi Ogawa

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415

DOI
10.1007/s00526-008-0166-5

SPRINGER

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
(T)integral(0) parallel to del u(tau)parallel to(B) (M) (2)(Or) d tau
where B M O(r) 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.

Web of Science ® 被引用回数 : 1

リンク情報
DOI
https://doi.org/10.1007/s00526-008-0166-5
Web of Science