Abstract
We prove that if u∈BV(Ω) is a local minimum for the non-parametric functional F(u) associated to a parametric integrand g∶Ω×ℝ×ℝn+1→[0,+∞), then the hypograph of u is locally minimizing for the parametric functionalG associated to g, among the sets of finite perimeter in Ω×ℝ.
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Anzellotti, G. Parametric and non-parametric minima. Manuscripta Math 48, 103–115 (1984). https://doi.org/10.1007/BF01169003
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DOI: https://doi.org/10.1007/BF01169003