2018/10/19 by Fanghua Lin, Lin, Fanghua, Changyou Wang +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1810.08348
This is in the sequel of authors' paper \citeLPW in which we 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. We 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 \citeKRS1, KRS2 on the fast reaction, slow diffusion and motion by the mean curvature would be addressed.