A note on positivity of two-dimensional differential operators

We consider the two-dimensional differential operator A(t,x)u(t, x) = -a11 (t, x) utt - a22(t, x)uxx +σu defined on functions on the half-plane ℝ+ × ℝ with the boundary condition u(0, x) = 0, x ε ℝ where aii(t, x), i = 1, 2 are continuously differentiable and satisfy the uniform ellipticity condition a211(t, x) + a222(t, x) ≥ δ >,σ > 0: The structure of fractional spaces Eα,1 (L1 (ℝ+ × ℝ), A(t,x)) generated by the operator A(t,x) is investigated. The positivity of A(t,x) in L1 (W2α1 (ℝ+ × ℝ)) spaces is established. In applications, theorems on well-posedness in L1 (W2α1 (ℝ+ × ℝ)) spaces of elliptic problems are obtained. © 2017, University of Nis. All rights reserved.

Авторы
Ashyralyev A. 1, 2, 3 , Akturk S.4
Журнал
Издательство
University of Nis
Номер выпуска
14
Язык
Английский
Страницы
4651-4663
Статус
Опубликовано
Том
31
Год
2017
Организации
  • 1 Department of Mathematics, Near East University, TRNC, Mersin 10, Nicosia, Turkey
  • 2 Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
  • 3 Peoples Friendship University Russia, Ul Miklukho Maklaya 6, Moscow, 117198, Russian Federation
  • 4 Yakuplu, the Neighborhood Street Kubilay, Istanbul, 34524, Turkey
Ключевые слова
Fractional spaces; Green’s function; Hölder spaces; Positive operator
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6099/