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Cited by 37 publications
(23 citation statements)
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“…If M is given as graph of a regular function u: Ω -• R + on a domain Ω c R w , n > 2, then u provides an equilibrium for the potential energy g 7 under gravitational forces, has been solved by Bemelmans and Dierkes in [BD]. It was shown in [BD,Theorem 7] that the coincidence set {u = 0} of a minimizer u is non-empty provided that…”
mentioning
confidence: 99%
“…If M is given as graph of a regular function u: Ω -• R + on a domain Ω c R w , n > 2, then u provides an equilibrium for the potential energy g 7 under gravitational forces, has been solved by Bemelmans and Dierkes in [BD]. It was shown in [BD,Theorem 7] that the coincidence set {u = 0} of a minimizer u is non-empty provided that…”
mentioning
confidence: 99%
“…In the case that u ∈ C 1 ( ), the surface energy term E = e −u 1 + |Du| 2 d x may be simplified by writing v = e −u , so E = v 2 + |Dv| 2 d x, which bears a close resemblance to the integral v + |Dv| 2 /4 d x investigated in [Bemelmans and Dierkes 1987]; see also [Dierkes and Huisken 1990].…”
Section: The Energy In the Isothermal Casementioning
confidence: 94%
“…The established techniques used for finding existence and regularity for the incompressible model may be divided into two groups: classical PDE techniques for surfaces of prescribed mean curvature, as, for example, in [Ladyzhenskaya and Ural'tseva 1970;Huisken 1985;Gilbarg and Trudinger 2001, Chapter 16]; and functions of bounded variation and sets of finite perimeter setting for minimizing the energy, as, for example, in [Emmer 1973;Gerhardt 1974;Giusti 1980;Gonzalez et al 1980;Huisken 1985]. In contrast, results concerned with compressible liquids are very recent and comparatively few [Athanassenas and Finn 2006;Finn and Luli 2007].…”
Section: Introductionmentioning
confidence: 99%
“…The upper bound in the case = 0 was proved in [BD,Theorem 6]. The proof for ∈ (0; 1] is similar, so we omit the details.…”
Section: Now (8) With a = 1 + 1=n Implies The Lower Boundmentioning
confidence: 95%