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Алгебра и анализ, 2011, том 23, выпуск 3, страницы 150–174
(Mi aa1245)
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Эта публикация цитируется в 9 научных статьях (всего в 9 статьях)
Статьи
Parabolic equations with variably partially VMO coefficients
H. Dong Division of Applied Mathematics, Brown University, Providence, RI, USA
Аннотация:
The $W^{1,2}_p$-solvability of second-order parabolic equations in nondivergence form in the whole space is proved for $p\in(1,\infty)$. The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with direction allowed to depend on the cylinder. This extends a recent result by Krylov for elliptic equations. The novelty in the current paper is that the restriction $p>2$ is removed.
Ключевые слова:
second-order equations, vanishing mean oscillation, partially VMO coefficients, Sobolev spaces.
Поступила в редакцию: 20.01.2010
Образец цитирования:
H. Dong, “Parabolic equations with variably partially VMO coefficients”, Алгебра и анализ, 23:3 (2011), 150–174; St. Petersburg Math. J., 23:3 (2012), 521–539
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1245 https://www.mathnet.ru/rus/aa/v23/i3/p150
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Страница аннотации: | 386 | PDF полного текста: | 102 | Список литературы: | 67 | Первая страница: | 6 |
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