English

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.

Keywords

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}
}
R2 v1 2026-06-22T11:19:02.046Z