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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 1988, Issue 3, Pages 21–29
(Mi uzeru911)
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Mathematics
The smoothness of regular equations according to parameter
G. А. Karapetyan Yerevan State University
Abstract:
In the article the solution of smoothness of one of the classes of hypo elliptic equations according to $\lambda$ parameter has been proved. The following has been proved particularly. For example, if we have the equation $P(\lambda, D)u=f$. Let’s mark by $N(\lambda)$ the set of solutions of equation $P(\lambda, D)u=0$ from class $W_2^H(R^n)$. If the dimension of $N(\lambda)$ does not depend on $\lambda,$ then all the solutions of equation $P(\lambda, D)u = f$ that are orthogonal to $N(\lambda)$ are infinitely differentiable by $(x, \lambda)$.
Received: 03.05.1988 Accepted: 14.09.1988
Citation:
G. А. Karapetyan, “The smoothness of regular equations according to parameter”, Proceedings of the YSU, Physical and Mathematical Sciences, 1988, no. 3, 21–29
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https://www.mathnet.ru/eng/uzeru911 https://www.mathnet.ru/eng/uzeru/y1988/i3/p21
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Abstract page: | 43 | Full-text PDF : | 12 | References: | 13 |
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