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Algebra i Analiz, 2019, Volume 31, Issue 3, Pages 136–153 (Mi aa1655)  
This article is cited in 2 scientific papers (total in 2 papers)

Research Papers

Sharp estimates for the gradient of solutions to the heat equation

G. Kresina, V. Maz'yabcd

a Department of Mathematics Ariel University, Ariel 40700, Israel
b RUDN University, 6 Miklukho-Maklay St., 117198, Moscow, Russia
c Department of Mathematical Sciences, University of Liverpool, M&O Building, Liverpool, L69 3BX, UK
d Department of Mathematics, Linköping University, SE-58183 Linköping, Sweden
Full-text PDF (230 kB) Citations (2)
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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.
Keywords: heat equation, sharp pointwise estimates for the gradient, first and second boundary value problems.
Received: 06.06.2018
English version:
St. Petersburg Mathematical Journal, 2020, Volume 31, Issue 3, Pages 495–507
DOI: https://doi.org/10.1090/spmj/1610
Bibliographic databases:
Document Type: Article
MSC: Primary 35K05; Secondary 26D20
Language: English
Citation: G. Kresin, V. Maz'ya, “Sharp estimates for the gradient of solutions to the heat equation”, Algebra i Analiz, 31:3 (2019), 136–153; St. Petersburg Math. J., 31:3 (2020), 495–507
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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