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This article is cited in 35 scientific papers (total in 35 papers)
On a degenerating problem with directional derivative
V. G. Maz'ya
Abstract:
We study a problem with directional derivative for a second order elliptic equation. We assume that smooth compact submanifolds $\Gamma_0\supset\Gamma_1\supset\cdots\supset\Gamma_s$ have been selected from the boundary $\Gamma$, and that the vector field is tangent to $\Gamma_i$ ($i\leqslant s-1$) at points of $\Gamma_{i+1}$ and not tangent to $\Gamma_s$. We show that the problem has a unique solution, obtain estimates of the solutions in $L_p(\Gamma)$ ($1<p\leqslant\infty$), and prove that the inverse operator is compact.
Bibliography: 29 titles.
Received: 29.03.1971
Citation:
V. G. Maz'ya, “On a degenerating problem with directional derivative”, Mat. Sb. (N.S.), 87(129):3 (1972), 417–454; Math. USSR-Sb., 16:3 (1972), 429–469
Linking options:
https://www.mathnet.ru/eng/sm3133https://doi.org/10.1070/SM1972v016n03ABEH001435 https://www.mathnet.ru/eng/sm/v129/i3/p417
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Abstract page: | 359 | Russian version PDF: | 144 | English version PDF: | 7 | References: | 38 |
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