General elliptic boundary-value problems in Hörmander—Roitberg spaces
We study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution of such an equation can be represented as a composition of a weak solution of...
Збережено в:
| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Видавничий дім "Академперіодика" НАН України
2018
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| Назва видання: | Доповіді НАН України |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/132635 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | General elliptic boundary-value problems in Hörmander—Roitberg spaces / V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov // Доповіді Національної академії наук України. — 2018. — № 2. — С. 12-18. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form.
The main result is given as a factorization theorem. This theorem states that every weak solution of such an equation
can be represented as a composition of a weak solution of the corresponding isotropic equation in a canonical domain
and a quasiconformal mapping agreed with a matrix-valued measurable coefficient appearing in the divergence
part of the equation. The latter makes it possible, in particular, to remove the regularity restrictions on the boundary
in the study of boundary-value problems for such semilinear equations. |
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