Vol. 11, No. 8, 2018

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Rigidity of minimizers in nonlocal phase transitions

Ovidiu Savin

Vol. 11 (2018), No. 8, 1881–1900
DOI: 10.2140/apde.2018.11.1881
Abstract

We obtain the classification of certain global bounded solutions for semilinear nonlocal equations of the type

su = W(u) in n, with s (1 2,1),

where W is a double-well potential.

Keywords
nonlocal phase transitions, De Giorgi conjecture
Mathematical Subject Classification 2010
Primary: 35J61
Milestones
Received: 8 December 2016
Revised: 9 February 2018
Accepted: 9 April 2018
Published: 6 June 2018
Authors
Ovidiu Savin
Department of Mathematics
Columbia University
New York, NY
United States