Calculus of Variations and Partial Differential Equations
巻, 号, ページ
Vol. 50
No. 1
p. 1-68
出版年月
2014年
出版者
和文:
英文:
Springer
会議名称
和文:
英文:
開催地
和文:
英文:
アブストラクト
We give a new proof of Brakke's partial regularity theorem up to for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The new proof extends to a general flow whose velocity is the sum of the mean curvature and any given background flow field in a dimensionally sharp integrability class. It is a natural parabolic generalization of Allard's regularity theorem in the sense that the special time-independent case reduces to Allard's theorem.
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