MISC

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

33
4
開始ページ
391
終了ページ
415
記述言語
英語
掲載種別
DOI
10.1007/s00526-008-0166-5
出版者・発行元
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
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000259186500001&DestApp=WOS_CPL