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This article is cited in 37 scientific papers (total in 37 papers)
Solution of the Dirichlet problem for some equations of Monge–Aampére type
N. M. Ivochkina
Abstract:
The solvability of the problem
$$
F_m(u)=f(x,u,u_x)\geqslant\nu>0,\qquad u|_{\partial\Omega}=0,
$$
in $C^{l+2+\alpha}(\overline\Omega)$, $l\geqslant2$, is proved, where $F_m(u)$ is the sum of all the principal minors of order $m$ of the Hessian $F_n(u)\equiv\det(u_{xx})$, $\Omega$ is a bounded strictly convex region in $R^n$, $n\geq2$, with boundary $\partial\Omega$ of class $C^{l+2+\alpha}$, 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.
Received: 01.08.1984
Citation:
N. M. Ivochkina, “Solution of the Dirichlet problem for some equations of Monge–Aampére type”, Mat. Sb. (N.S.), 128(170):3(11) (1985), 403–415; Math. USSR-Sb., 56:2 (1987), 403–415
Linking options:
https://www.mathnet.ru/eng/sm2167https://doi.org/10.1070/SM1987v056n02ABEH003043 https://www.mathnet.ru/eng/sm/v170/i3/p403
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Abstract page: | 498 | Russian version PDF: | 151 | English version PDF: | 14 | References: | 74 | First page: | 1 |
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