2001/05/16 by Massimiliano Morini, Morini, Massimiliano
Chemistry · Decision Sciences · Mathematics · Physics and Astronomy · #49K10 #49Q20 #Chemical Thermodynamics and Molecular Structure #FOS: Mathematics #Functional Analysis (math.FA) #Radioactive Decay and Measurement Techniques #Scientific Measurement and Uncertainty Evaluation #math.FA #msc:49K10 #msc:49Q20
paper · pdf · doi:10.48550/arxiv.math/0105141
33 pages
arxiv created 2001/05/16 · openalex publication_date 2001/05/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a calibration method we prove that, if Γ⊂ Ω is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function uβ which solves \begincases Δuβ=β(uβ-g)amp; in Ω∖Γ ∂ν uβ=0 amp; on ∂Ω∪Γ \endcases is in turn discontinuous along Γ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional ∫Ω∖ Su|∇ u|2 dx +\cal Hn-1(Su)+β∫Ω∖ Su(u-g)2 dx, over SBV(Ω), for β large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.