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On the convergence of stable phase transitions

โœ Scribed by Pablo Padilla; Yoshihiro Tonegawa

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
479 KB
Volume
51
Category
Article
ISSN
0010-3640

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โœฆ Synopsis

We consider the local behavior of critical points of the functional

Here, W is a double-well potential and U is a regular domain in R n , n โ‰ฅ 2. Assuming that {u ฮต }ฮต>0 is stable for n = 2 and locally energy-minimizing for n = 3, we show that the level sets of solutions converge in an average sense to a stationary (n -1)-rectifiable varifold.

Our study is based on estimates derived from the second variation formula and is entirely local.

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