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Sbornik: Mathematics, 2002, Volume 193, Issue 9, Pages 1243–1279
DOI: https://doi.org/10.1070/SM2002v193n09ABEH000677 (Mi sm677) 		 
This article is cited in 4 scientific papers (total in 4 papers)

$L_p$-solubility of the Dirichlet problem for the heat equation in non-cylindrical domains

Yu. A. Alkhutov

Vladimir State Pedagogical University
English version PDF (345 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM2002v193n09ABEH000677
Abstract: The Dirichlet problem for the heat equation is considered in bounded and unbounded domains of paraboloid type with isolated characteristic points at the boundary. Necessary and sufficient conditions in terms of the weight ensuring the unique solubility of this problem in weighted Sobolev $L_p$-spaces are found. In particular, a criterion for the solubility of the problem in the classical Sobolev space $W_{p,0}^{2,1}$ is established in the case when the domain is a ball.
Received: 14.06.2001
Russian version:
Matematicheskii Sbornik, 2002, Volume 193, Number 9, Pages 3–40
DOI: https://doi.org/10.4213/sm677
Bibliographic databases:
UDC: 517.946
MSC: 35K05, 35K20
Language: English
Original paper language: Russian
Citation: Yu. A. Alkhutov, “$L_p$-solubility of the Dirichlet problem for the heat equation in non-cylindrical domains”, Mat. Sb., 193:9 (2002), 3–40; Sb. Math., 193:9 (2002), 1243–1279
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:65
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