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

Fang-Hua Lin, Changyou Wang

Research output: Contribution to journalArticle

Abstract

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
Volume40
Issue number5
DOIs
StatePublished - Sep 1 2019

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Gradient Flow
Potential Well
Harmonic Maps
Mean Curvature
High-dimensional
Phase Transition
Phase transitions
Regularity Theory
Motion
Boundary conditions
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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells. / Lin, Fang-Hua; Wang, Changyou.

In: Chinese Annals of Mathematics. Series B, Vol. 40, No. 5, 01.09.2019, p. 781-810.

Research output: Contribution to journalArticle

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