# American Institute of Mathematical Sciences

December  2007, 19(4): 777-798. doi: 10.3934/dcds.2007.19.777

## The geometry of mesoscopic phase transition interfaces

 1 Dipartimento di Matematica Università di Pisa, Via Buonarroti 2, I-56127 Pisa, Italy 2 Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, I-00133 Roma, Italy

Received  November 2006 Revised  March 2007 Published  September 2007

We consider a mesoscopic model of phase transitions and investigate the geometric properties of the interfaces of the associated minimal solutions. We provide density estimates for level sets and, in the periodic setting, we construct minimal interfaces at a universal distance from any given hyperplane.
Citation: Matteo Novaga, Enrico Valdinoci. The geometry of mesoscopic phase transition interfaces. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 777-798. doi: 10.3934/dcds.2007.19.777
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