Sharp pointwise estimates for the gradients of solutions to linear parabolic second-order equation in the layer

We deal with solutions of the Cauchy problem to linear both homogeneous and nonhomogeneous parabolic second-order equations with real constant coefficients in the layer ℝn+1 T=ℝn×(0,T), where n≥1 and T<∞. The homogeneous equation is considered with initial data in Lp(ℝn),1 ≥ p ≥ ∞. For the nonhomogeneous equation we suppose that initial function is equal to zero and the function in the right-hand side belongs to (Formula presented.), p>n + 2 and α ∈ (0,1). Explicit formulas for the sharp coefficients in pointwise estimates for the length of the gradient to solutions to these problems are obtained. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.

Авторы
Kresin G.1 , Maz'ya V. 2, 3, 4
Редакторы
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Журнал
Издательство
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Номер выпуска
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Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
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Номер
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Том
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Год
2020
Организации
  • 1 Department of Mathematics, Ariel University, Ariel, Israel
  • 2 Department of Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom
  • 3 Department of Mathematics, Linköping University, Linköping, Sweden
  • 4 RUDN University, Moscow, Russian Federation
Ключевые слова
Cauchy problem; parabolic equation of the second order with constant coefficients; pointwise estimates for the gradient; Primary: 35K15; Robert Pertsch Gilbert; Secondary: 35E99
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/65545/