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Eurasian Mathematical Journal, 2010, том 1, номер 1, страницы 54–72
(Mi emj7)
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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations
H. G. Ghazaryan, V. N. Margaryan Department of mathematics and mathematical modelling, Russian–Armenian (Slavonic) State University, Yerevan, Armenia
Аннотация:
A linear differential operator $P(D)$ with constant coefficients is called almost hypoelliptic if all derivatives $P^{(\nu)}(\xi)$ of the characteristic polynomial $P(\xi)$ can be estimated above via $P(\xi)$. In this paper it is proved that all solutions of the equation $P(D)u=f$ where $f$ and all its derivatives are square integrable with a certain exponential weight, which are square integrable with the same weight, are also such that all their derivatives are square integrable with this weight, if and only if the operator $P(D)$ is almost hypoelliptic.
Ключевые слова и фразы:
hypoelliptic operator (polynomial), almost hypoelliptic operator (polynomial), weighted Sobolev spaces.
Поступила в редакцию: 25.12.2009
Образец цитирования:
H. G. Ghazaryan, V. N. Margaryan, “On infinite differentiability of solutions of nonhomogeneous almost hypoelliptic equations”, Eurasian Math. J., 1:1 (2010), 54–72
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj7 https://www.mathnet.ru/rus/emj/v1/i1/p54
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Страница аннотации: | 386 | PDF полного текста: | 109 | Список литературы: | 56 |
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