Abstract
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.
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© 1984 Springer Science+Business Media New York
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Giusti, E. (1984). Direct Methods. In: Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol 80. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-9486-0_14
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DOI: https://doi.org/10.1007/978-1-4684-9486-0_14
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3153-6
Online ISBN: 978-1-4684-9486-0
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