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| Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells |
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Citation： |
Fanghua LIN,Changyou WANG.Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells[J].Chinese Annals of Mathematics B,2019,40(5):781~810 |
| Page view： 621
Net amount： 423 |
Authors： |
Fanghua LIN; Changyou WANG |
Foundation： |
This work was supported by NSF Grants DMS-1501000,
DMS-1764417. |
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| 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, {\it Comm. Pure Appl. Math.}, {\bf 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. |
Keywords： |
Partially free and partially constrained boundary, Boundary partialregularity, Boundary monotonicity inequality |
Classification： |
35J50 |
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