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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 115, Pages 178–190
(Mi znsl4050)
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This article is cited in 2 scientific papers (total in 2 papers)
Solvability of the Dirichlet problem for degenerate quasilinear elliptic equations
P. Z. Mkrtychyan
Abstract:
In a bounded domain of the n-dimensional
$$
\sum_{i=1}^n\frac\partial{\partial x_i}(a^{l_i}(u)|u_{x_i}|^{m_i-2}u_{x_i})=f(x),
$$
where $x=(x_1,\dots,x_n)$, $l_i\ge0$, $m_i>1$, the function $f$ is summable with some power, the nonnegative continuous function $a(u)$ vanishes at a finite number of points and satisfies $\varliminf_{|u|\to\infty}a(u)>0$. One proves the existence of bounded generalized solutions with a finite integral
$$
\int_\Omega\sum_{i=1}^na^{l_i}(u)|u_{x_i}|^{m_i}\,dx
$$
of the Dirichlet problem with zero boundary conditions.
Citation:
P. Z. Mkrtychyan, “Solvability of the Dirichlet problem for degenerate quasilinear elliptic equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 178–190; J. Soviet Math., 28:5 (1985), 742–750
Linking options:
https://www.mathnet.ru/eng/znsl4050 https://www.mathnet.ru/eng/znsl/v115/p178
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Abstract page: | 98 | Full-text PDF : | 35 |
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