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Mat. Sb., 2002, Volume 193, Number 9, Pages 3–40 (Mi msb677)  

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

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.

DOI: https://doi.org/10.4213/sm677

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English version:
Sbornik: Mathematics, 2002, 193:9, 1243–1279

Bibliographic databases:

UDC: 517.946
MSC: 35K05, 35K20
Received: 14.06.2001

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Alkhutov, L. I. Kurlykova, “L p -solvability of the Dirichlet problem for the heat equation in noncylindrical domains with isolated characteristic points at the boundary”, J Math Sci, 2011  crossref  mathscinet  scopus  scopus  scopus
    2. Kheloufi A., “Resolutions of Parabolic Equations in Non-Symmetric Conical Domains”, Electron. J. Differ. Equ., 2012, 116  mathscinet  zmath  isi  elib
    3. Arezki Kheloufi, Boubaker-Khaled Sadallah, “Study of the heat equation in a symmetric conical type domain of RN+1”, Math. Meth. Appl. Sci, 2013, n/a  crossref  mathscinet  scopus  scopus  scopus
    4. Kheloufi A., “Parabolic Equations With Cauchy-Dirichlet Boundary Conditions in a Non-Regular Domain of Rn+1”, Georgian Math. J., 21:2 (2014), 199–209  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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