Abstract:
The solvability of the problem
Fm(u)=f(x,u,ux)⩾ν>0,u|∂Ω=0,
in Cl+2+α(¯Ω), l⩾2, is proved, where Fm(u) is the sum of all the principal minors of order m of the Hessian Fn(u)≡det(uxx), Ω is a bounded strictly convex region in Rn, n≥2, with boundary ∂Ω of class Cl+2+α, for m=1,2,3,n, under certain restrictions on the occurrence of u and p as arguments in f(x,u,p).
Bibliography: 21 titles.
\Bibitem{Ivo85}
\by N.~M.~Ivochkina
\paper Solution of the Dirichlet problem for some equations of Monge--Aamp\'ere type
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 2
\pages 403--415
\mathnet{http://mi.mathnet.ru/eng/sm2167}
\crossref{https://doi.org/10.1070/SM1987v056n02ABEH003043}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=815272}
\zmath{https://zbmath.org/?q=an:0609.35042}
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This publication is cited in the following 38 articles:
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Zedong Yang, Zhanbing Bai, “Multiplicity of k-convex solutions for a singular k-Hessian system”, Demonstratio Mathematica, 57:1 (2024)
Chuanqiang Chen, Li Chen, Xinqun Mei, Ni Xiang, “The Neumann problem for a class of mixed complex Hessian equations”, DCDS, 42:9 (2022), 4203
Kazuhiro Takimoto, “Bernstein type theorem for the generalized parabolic 2-Hessian equation under weaker conditions”, Journal of Mathematical Analysis and Applications, 495:1 (2021), 124703
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N. M. Ivochkina, “From Gårding's cones to $p$-convex hypersurfaces”, Journal of Mathematical Sciences, 201:5 (2014), 634–644