Singular perturbation problems with a compact support semilinear term

Article type: Research Article

Authors: Alberti, Giovanni^; | Ambrosio, Luigi | Buttazzo, Giuseppe

Affiliations: Instituto di Matematiche Applicate, Via Bonanno 25/B, 56126 Pisa, Italy | Dipartimento di Matematica, Via Buonarroti 2, 56127 Pisa, Italy

Note: [] Correspondence to: G. Alberti, Instituto di Matematiche Applicate, Via Bonanno 25/B, 56126 Pisa, Italy.

Abstract: In this paper we study the asymptotic behaviour of the functionals Fε(u)=∫Ω[ε|∇u|2+ε−3β(u/ε)]dx where β is a non-negative lower semicontinuous function with compact support. When ε tends to 0, the limit functional corresponds to a least area problem with an obstacle.

DOI: 10.3233/ASY-1994-8303

Journal: Asymptotic Analysis, vol. 8, no. 3, pp. 247-258, 1994