The geometry of mesoscopic phase transition interfaces

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

The geometry of mesoscopic phase transition interfaces

Matteo Novaga ^1, and Enrico Valdinoci ^2,

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

Abstract
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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.

Keywords: plane-like solutions., Ginzburg-Landau-Allen-Cahn equation, density estimates.

Mathematics Subject Classification: Primary: 35B10, 35B15, 35B27; Secondary: 35J20, 35Q72, 49S0.

Citation: Matteo Novaga, Enrico Valdinoci. The geometry of mesoscopic phase transition interfaces. Discrete & Continuous Dynamical Systems - A, 2007, 19 (4) : 777-798. doi: 10.3934/dcds.2007.19.777

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