Higher dimensional Ginzburg-Landau equations under weak anchoring boundary conditions

2017/10/31 by Bauman, Patricia, Phillips, Daniel, Wang, Changyou
#35J57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.11437

Abstract

For n≥ 3 and 00 and α∈ [0,1), and g_ε∈ C²(∂Ω, \mathbb S¹). Motivated by the connection with the Landau-De Gennes model of nematic liquid crystals under weak anchoring conditions, we study the asymptotic behavior of u_ε as ε goes to zero under the condition that the total modified Ginzburg-Landau energy satisfies F_ε(u_ε,Ω)≤ M|logε| for some M>0.

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