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arXiv · 1510.03651

Counterexamples to Modica's gradient estimate for systems arising in multi-phase transitions

Christos Sourdis
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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.

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Christos Sourdis. 2015-10-13. Counterexamples to Modica's gradient estimate for systems arising in multi-phase transitions. https://arxiv.org/abs/1510.03651

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