Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells

Fanghua Lin, Changyou Wang

Research output: Contribution to journalArticlepeer-review


This is in the sequel of authors’ paper [Lin, F. H., Pan, X. B. and Wang, C. Y., Phase transition for potentials of high dimensional wells, Comm. Pure Appl. Math., 65(6), 2012, 833-888] in which the authors had set up a program to verify rigorously some formal statements associated with the multiple component phase transitions with higher dimensional wells. The main goal here is to establish a regularity theory for minimizing maps with a rather non-standard boundary condition at the sharp interface of the transition. The authors also present a proof, under simplified geometric assumptions, of existence of local smooth gradient flows under such constraints on interfaces which are in the motion by the mean-curvature. In a forthcoming paper, a general theory for such gradient flows and its relation to Keller-Rubinstein-Sternberg’s work (in 1989) on the fast reaction, slow diffusion and motion by the mean curvature would be addressed.

Original languageEnglish (US)
Pages (from-to)781-810
Number of pages30
JournalChinese Annals of Mathematics. Series B
Issue number5
StatePublished - Sep 1 2019


  • 35J50
  • Boundary monotonicity inequality
  • Boundary partial regularity
  • Partially free and partially constrained boundary

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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