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Mat. Sb., 1989, Volume 180, Number 7, Pages 867–887 (Mi msb1639)  

This article is cited in 15 scientific papers (total in 15 papers)

Solution of the Dirichlet problem for curvature equations of order $m$

N. M. Ivochkina

Abstract: Solvability conditions for curvature equations of order which are sufficient, and almost necessary, are obtained, and theorems concerning the existence of solutions in $C^{l+2+\alpha}(\overline\Omega)$, $l\geqslant2$, $0<\alpha<1$, are proved. The first-order curvature equation coincides with the curvature equation of order $m$, and the curvature equation of order $n$ with the Monge–Ampère equation.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1990, 67:2, 317–339

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J65; Secondary 53C45
Received: 04.02.1987 and 05.01.1988

Citation: N. M. Ivochkina, “Solution of the Dirichlet problem for curvature equations of order $m$”, Mat. Sb., 180:7 (1989), 867–887; Math. USSR-Sb., 67:2 (1990), 317–339

Citation in format AMSBIB
\by N.~M.~Ivochkina
\paper Solution of the Dirichlet problem for curvature equations of order~$m$
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 7
\pages 867--887
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 2
\pages 317--339

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    This publication is cited in the following articles:
    1. Trudinger N., “A-Priori Bounds and Necessary Conditions for Solvability of Prescribed Curvature Equations”, Manuscr. Math., 67:1 (1990), 99–112  crossref  mathscinet  zmath  isi
    2. Mi Lin, Neil S. Trudinger, “On some inequalities for elementary symmetric functions”, BAZ, 50:2 (1994), 317  crossref
    3. Ivochkina N., Ladyzhenskaya O., “The First Initial-Boundary Value-Problem for Evolutionary Equations Generated by Symmetrical Functions of the Principal Curvatures”, Dokl. Akad. Nauk, 340:2 (1995), 155–157  mathnet  mathscinet  zmath  isi
    4. Ivochkina N., Tomi F., “Locally Convex Hypersurfaces of Prescribed Curvature and Boundary”, Calc. Var. Partial Differ. Equ., 7:4 (1998), 293–314  crossref  mathscinet  zmath  isi
    5. Bo Guan, Joel Spruck, “Locally convex hypersurfaces of constant curvature with boundary”, Comm Pure Appl Math, 57:10 (2004), 1311  crossref  mathscinet  zmath  elib
    6. Sheng W., Urbas J., Wang X., “Interior Curvature Bounds for a Class of Curvature Equations”, Duke Math. J., 123:2 (2004), 235–264  crossref  mathscinet  zmath  isi
    7. Eric T. Sawyer, Richard L. Wheeden, “Regularity of Degenerate Monge–Ampère and Prescribed Gaussian Curvature Equations in Two Dimensions”, Potential Anal, 24:3 (2006), 267  crossref  mathscinet  zmath  isi
    8. Pierre Bayard, Philippe Delanoë, “Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature”, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 26:3 (2009), 903  crossref
    9. V. N. Kokarev, “Smeshannye formy ob'ema i kompleksnoe uravnenie tipa Monzha–Ampera na tore”, Vestn. SamGU. Estestvennonauchn. ser., 2009, no. 8(74), 35–43  mathnet
    10. V. N. Kokarev, “Mixed volume forms and a complex equation of Monge–Ampère type on Kähler manifolds of positive curvature”, Izv. Math., 74:3 (2010), 501–514  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. N. M. Ivochkina, S. I. Prokof’eva, G. V. Yakunina, “The Gårding cones in the modern theory of fully nonlinear second order differential equations”, J Math Sci, 184:3 (2012), 295  crossref
    12. Yong Huang, Lu Xu, “Two problems related to prescribed curvature measures”, DCDS-A, 33:5 (2012), 1975  crossref
    13. N. M. Ivochkina, “From Gårding's cones to $p$-convex hypersurfaces”, Journal of Mathematical Sciences, 201:5 (2014), 634–644  mathnet  crossref  mathscinet
    14. Enache C., “Maximum and Minimum Principles for a Class of Monge-Ampere Equations in the Plane, with Applications to Surfaces of Constant Gauss Curvature”, Commun. Pure Appl. Anal, 13:3 (2014), 1347–1359  crossref  isi
    15. Covei D.-P., “a Necessary and a Sufficient Condition For the Existence of the Positive Radial Solutions To Hessian Equations and Systems With Weights”, Acta Math. Sci., 37:1 (2017), 47–57  mathscinet  isi
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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