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The Dirichlet problem for the equation of prescribed Gauss curvature. (English) Zbl 0524.35047


MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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References:

[1] Aleksandrov, Vestnik Leningrad Univ. Math. 21 pp 5– (1966)
[2] Aleksandrov, Vestnik Leningrad Univ. Math. 13 pp 5– (1958)
[3] DOI: 10.1016/0022-1236(81)90081-1 · Zbl 0465.35001 · doi:10.1016/0022-1236(81)90081-1
[4] DOI: 10.2307/1999182 · Zbl 0518.35036 · doi:10.2307/1999182
[5] DOI: 10.1098/rsta.1969.0033 · Zbl 0181.38003 · doi:10.1098/rsta.1969.0033
[6] Lions, Arch. Rat. Mech. Anal.
[7] Bakel’man, Dokl. Akad. Nauk SSSR 126 pp 923– (1959)
[8] DOI: 10.1002/cpa.3160300104 · Zbl 0347.35019 · doi:10.1002/cpa.3160300104
[9] Gilbarg, Elliptic partial differential equations of second order (1983) · Zbl 0562.35001 · doi:10.1007/978-3-642-61798-0
[10] Caffarelli, Comm. Pure Appl. Math.
[11] Bakel’man, Siberian Math. J. 4 pp 206– (1963)
[12] Bakel’man, Geometric methods for solving elliptic equations (1965)
[13] DOI: 10.1007/BF01165928 · Zbl 0509.35036 · doi:10.1007/BF01165928
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