Singularity sets for solutions equations of maximal surfaces in Minkowski space. (English. Russian original) Zbl 0834.35025
Sib. Math. J. 33, No. 6, 1066-1075 (1992); translation from Sib. Mat. Zh. 33, No. 6, 131-140 (1992).
See the review in Zbl 0805.35014.
MSC:
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
Citations:
Zbl 0805.35014References:
| [1] | B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Nauka, Moscow (1985). |
| [2] | K. Ecker, ?Area maximizing hypersurfaces in Minkowski space having an isolated singularity,? Manuscripta Math.,56, No. 4, 375-397 (1986). · Zbl 0594.58023 · doi:10.1007/BF01168501 |
| [3] | D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order [Russian translation], Nauka, Moscow (1989). · Zbl 0691.35001 |
| [4] | V. A. Klyachin and V. M. Miklyukov, ?Maximal hypersurfaces of tubular type in the Minkowski space,? Izv. Akad. Nauk SSSR Ser. Mat.,55, No. 1, 206-217 (1991). · Zbl 0732.53049 |
| [5] | J. C. C. Nitsche, ?On new results in the theory of minimal surface,? Bull. Amer. Math. Soc.,71, No. 2, 195-270 (1965). · Zbl 0135.21701 · doi:10.1090/S0002-9904-1965-11276-9 |
| [6] | A. De Giorge and G. Stampacchia, ?Sulle singolarit? eleminabili ipersuperficie minimali,? Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (8),38 79-85 (1965). |
| [7] | Yu. G. Reshetnyak, ?The concept of capacity in the theory of functions with generalized derivatives,? Sibirsk. Mat. Zh.,10, No. 5, 1109-1136 (1969). |
| [8] | A. A. Klyachin and V. M. Miklyukov, ?Spacelike hypersurfaces and the problem of extension of functions with gradient constraint,? Dokl. Akad. Nauk SSSR,320, No. 4, 781-784 (1991). · Zbl 0769.49032 |
| [9] | R. Bartnik and L. Simon, ?Spacelike hypersurfaces with prescribed boundary values and mean curvature,? Comm. Math. Phys.,27, No. 1, 131-152 (1982). · Zbl 0512.53055 · doi:10.1007/BF01211061 |
| [10] | A. A. Klyachin and V. M. Miklyukov, ?On existence and uniqueness in the Dirichlet problem for the equation of maximal surfaces with singularities,? in: Abstracts. Proc. Scientific Conference [in Russian], Volgograd Univ., Volgograd, 1990, p. 87. |
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