Аннотация:
Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space Lp. Derivation of the coefficients is based on solving certain optimization problems with respect to a vector parameter inside of an integral over the unit sphere.
Ключевые слова:
heat equation, sharp pointwise estimates for the gradient, first and second boundary value problems.
Образец цитирования:
G. Kresin, V. Maz'ya, “Sharp estimates for the gradient of solutions to the heat equation”, Алгебра и анализ, 31:3 (2019), 136–153; St. Petersburg Math. J., 31:3 (2020), 495–507
\RBibitem{KreMaz19}
\by G.~Kresin, V.~Maz'ya
\paper Sharp estimates for the gradient of solutions to the heat equation
\jour Алгебра и анализ
\yr 2019
\vol 31
\issue 3
\pages 136--153
\mathnet{http://mi.mathnet.ru/aa1655}
\elib{https://elibrary.ru/item.asp?id=43290419}
\transl
\jour St. Petersburg Math. J.
\yr 2020
\vol 31
\issue 3
\pages 495--507
\crossref{https://doi.org/10.1090/spmj/1610}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000531807300007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085768928}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1655
https://www.mathnet.ru/rus/aa/v31/i3/p136
Эта публикация цитируется в следующих 2 статьяx:
Kresin G., Maz'ya V., “Sharp Pointwise Estimates For the Gradients of Solutions to Linear Parabolic Second-Order Equation in the Layer”, Appl. Anal., 101:1 (2022), 136–145
Kresin G., Maz'ya V., “Sharp Pointwise Estimates For Solutions of Weakly Coupled Second-Order Parabolic System in a Layer”, Complex Var. Elliptic Equ., 66:6-7 (2021), 945–963