Part of the Monographs in Mathematics book series (MMA, volume 80)
An alternative approach to the existence of non-parametric minimal surfaces with prescribed boundary data consists in using direct methods in the calculus of variations to minimize the area integrand among all the functions taking prescribed values ϕ(x) on ∂Ω. As for the parametric case, the natural space here is BV(Ω), the space of functions whose derivatives are Radon measures in Ω.
KeywordsMinimal Surface Dirichlet Problem Radon Measure Natural Space Strong Maximum Principle
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© Springer Science+Business Media New York 1984