| Autor: |
Grafke, Tobias, Scholtes, Sebastian, Wagner, Alfred, Westdickenberg, Maria G. |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, Ren, and Vanden-Eijnden -- a numerical algorithm for computing transition pathways in complex systems -- in $d=2$ to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical observations, we adapt a method of Caffarelli and Spruck to study convexity of level sets in $d\geq 2$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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