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Souček, Vladimír
The nonexistence of a weak solution of Dirichlet's problem for the functional of minimal surface on nonconvex domains. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 12 (1971), issue 4, pp. 723-736
MSC: 35D05, 35J25, 35J60, 35J67, 49F10, 49Q05, 53A10 | MR 0296786 | Zbl 0256.35030
References:
[1] R. FINN: Remark relevant to minimal surfaces and to surface of prescribed mean curvature. Journal d'Analyse Mathematique 14 (1965), 139-160. MR 0188909
[2] J. SOUČEK: The spaces of the functions on domain $\Omega $, whose k-th derivatives are measure, defined on $\overline \Omega $. - to appear in Czech. Math. Journ. MR 0313798
[3] J KAČÚR J. NEČAS J. SOUČEK: The ultraweak solutions of variational problems over spaces $W_1^(k) $ of the types of nonparametric minimal surface. - to appear.
[4] J. C. C. NITSCHE: On new results in the theory of minimal surfaces. Bull. Amer. math. Soc. 71 (1965), 195-270. MR 0173993 | Zbl 0135.21701
[5] H. JENKINS J. SERRIN: Variational problems of minimal surface type II. Arch. Rat. Mech. Anal. 21 (1966), 321-342. MR 0190811
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