A general regularity theory for weak mean curvature flow

• Kasai, Kota

• Tonegawa, Yoshihiro

Abstract

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.

Journal

• Calculus of Variations and Partial Differential Equations

  Calculus of Variations and Partial Differential Equations 50 (1-2), 1-68, 2014-05-01

  Springer

Details

• CRID: 1050001339016764928
• NII Article ID: 120005600747
• ISSN: 14320835
• ISSN: 09442669
• HANDLE: 2115/58534
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles