Anisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionals

• Published in: ESAIM. Control, optimisation and calculus of variations Vol. 24; no. 3; pp. 1107 - 1139
• Main Author: Bach, Annika
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 2018
• Subjects: 49J45; 68U10; 74G65; Ambrosio-Tortorelli approximation; anisotropic free-discontinuity functionals; Control theory; Discontinuity; Finsler metrics; Mathematical analysis; Γ-convergence

We provide an approximation result for free-discontinuity functionals of the form         𝓕(u) = ∫Ωf(x, u, ∇u)dx + ∫Su∩Ωθ(x, νu)d𝓗n−1,     u ∈ SBV2(Ω), where f is quadratic in the gradient-variable and θ is an arbitrary smooth Finsler metric. The approximating functionals are of Ambrosio-Tortorelli...