Counterexamples to Modica's gradient estimate for systems arising in multi-phase transitions
Analysis of PDEs
2015-10-14 v1
Abstract
We construct a plethora of one-dimensional periodic solutions for a class of semilinear elliptic systems of phase transition type which violate Modica's gradient estimate. This complements a recent technical counterexample in arXiv:1401.4847 and is partly motivated by a recent open problem in arXiv:1506.02731.
Cite
@article{arxiv.1510.03651,
title = {Counterexamples to Modica's gradient estimate for systems arising in multi-phase transitions},
author = {Christos Sourdis},
journal= {arXiv preprint arXiv:1510.03651},
year = {2015}
}