Density estimates for a variational model driven by the Gagliardo norm

2010/07/13 by Savin, Ovidiu, Valdinoci, Enrico · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.2114

Abstract

We prove density estimates for level sets of minimizers of the energy \eps^2s‖u‖_H^s(Ω)²+∫_ΩW(u) dx, with s ∈ (0,1), where ‖u‖_H^s(Ω) denotes the total contribution from Ω in the H^s norm of u, and W is a double-well potential. As a consequence we obtain, as \eps → 0, the uniform convergence of the level sets of u to either a H^s-nonlocal minimal surface if s∈(0,\frac 1 2), or to a classical minimal surface if s ∈[\frac 1 2,1).

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• Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (I): The De Giorgi conjecture for the local problem in ℝ³
• Γ-convergence for nonlocal phase transitions involving the H^1/2 norm

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