Sharp estimates for the gradient of solutions to the heat equation
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- by G. Kresin and V. Maz′ya
- St. Petersburg Math. J. 31 (2020), 495-507
- DOI: https://doi.org/10.1090/spmj/1610
- Published electronically: April 30, 2020
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Abstract:
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 $L^p$. 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.References
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Bibliographic Information
- G. Kresin
- Affiliation: Department of Mathematics, Ariel University, Ariel 40700, Israel
- Email: kresin@ariel.ac.il
- V. Maz′ya
- Affiliation: Department of Mathematical Sciences, University of Liverpool, M&O Building, Liverpool, L69 3BX, UK; Department of Mathematics, Linköping University, SE-58183 Linköping, Sweden; RUDN University, 6 Miklukho-Maklay St., 117198 Moscow, Russia
- MR Author ID: 196507
- Email: vladimir.mazya@liu.se
- Received by editor(s): June 6, 2018
- Published electronically: April 30, 2020
- © Copyright 2020 American Mathematical Society
- Journal: St. Petersburg Math. J. 31 (2020), 495-507
- MSC (2010): Primary 35K05; Secondary 26D20
- DOI: https://doi.org/10.1090/spmj/1610
- MathSciNet review: 3985922
Dedicated: In memory of Solomon G. Mikhlin