Affiliations: Istituto di Matematica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/a, 50139 Firenze, Italy | Dipartimento di Matematica e Applicazioni, Complesso Monte S. Angelo, Ed. T, Via Anzia, 80126 Napoli, Italy
Note: [] Correspondence to: E. Mascolo, Istituto di Matematica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/a, 50139 Firenze, Italy.
Abstract: We study the asymptotic behaviour of the minimizers of the variational problem: min {∫a−a[ε2(u′)2(x)+W(u(x))]dx:u∈L1(−a,a),u≥0,∫a−au(x)dx=m,u(−a)=u(a)=c}, where m/2a∈(α,β) and W is a non-negative, continuous and non-convex function, with W(u) = 0 iff u∈{α,β}. We prove that the presence of the necking is related to the value c; more precisely, we have a “neck” if c<α and a “buldge” if c>β.
