Rigidity of minimizers in nonlocal phase transitions II

2018/02/05 by Savin, Ovidiu · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.01710

Abstract

In this paper we extend the results of \citeS3 to the borderline case s = \frac 12. We obtain the classification of global bounded solutions with asymptotically flat level sets for semilinear nonlocal equations of the type Δ^{\frac 12} u=W'(u) in Rⁿ, where W is a double well potential.

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• Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (II): The De Giorgi conjecture for the nonlocal problem in ℝ² or ℝ³
• Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (I): The De Giorgi conjecture for the local problem in ℝ³

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