The geometry of mesoscopic phase transition interfaces

Matteo Novaga; Enrico Valdinoci

doi:10.3934/dcds.2007.19.777

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2007, Volume 19, Issue 4: 777-798. Doi: 10.3934/dcds.2007.19.777

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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
2.
Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, I-00133 Roma

Received: November 2006

Revised: March 2007

Published: October 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B10, 35B15, 35B27; Secondary: 35J20, 35Q72, 49S05.

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