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Estimates of Green's function of homogeneous first-boundary problem for a second-order parabolic equation in a noncylindrical region

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Literature cited

  1. P. E. Sobolevskii, “Estimates of Green's function of parabolic second-order partial differential equations,” Dokl. Akad. Nauk SSSR,138, No. 2 (1961).

  2. S. D. Ivasishen, “Estimates of derivatives of Green's function of the first boundary problem for a second-order parabolic equation,” Abstracts of papers of 22nd Scientific Session, Physical and Mathematical Sciences Section, Chernovtsy (1966).

    Google Scholar 

  3. Reiko Arima, “On general boundary value problem for parabolic equations,” Journ. Math. Kyoto Univ.,4, No. 1, 207–243 (1964).

    Google Scholar 

  4. S. D. Gidelman and S. D. Ivasishen, “Estimates of derivatives of Green's matrix for a parabolic boundary problem,” Dokl. Akad. Nauk URSR, No. 7 (1966).

  5. S. D. Ivasishen and S. D. Éidel'man, “Estimates of Green's matrix of a homogeneous parabolic boundary problem,” Dokl. Akad. Nauk SSSR,172, No. 6 (1967).

  6. A. Friedman, “Boundary estimates for second-order parabolic equations and their application,” Journ. Math. and Mech.,7, No.5, 771–791 (1958).

    Google Scholar 

  7. L. I. Kamynin, “On the smoothness of thermal potentials,” Dif. Uravneniya,1, No. 6 (1965).

  8. S. D. Éidel'man, Parabolic Systems [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  9. S. D. Ivasishen and S. D. Éidel'man, “→2b-parabolic systems,” Transactions of Seminar on Functional Analysis, Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, No. 1, Kiev (1966).

    Google Scholar 

  10. W. Pogorzelski, “Étude d'une fonction de Green et du probleme aux limites pour l'équation parabolique normale,” Ann. Polon. Math.,4, No. 3, 288–307 (1958).

    Google Scholar 

  11. A. M. Il'in, A. S. Kalashnikov, and O. A. Oleinik, “Linear second-order parabolic equations,” Ukr. Matern. Zh.,17, No. 3, 105 (1962).

    Google Scholar 

  12. A. Piskorek, “Propriétes d'une integrale de l'équation parabolique dans un domaine noncylindrique,” Ann. Polon. Math.,8, 125–137 (1960).

    Google Scholar 

  13. B. Ya. Lipko, “Application of potentials in establishing the solvability of parabolic boundary problems for regions of general form” [in Russian], Author's abstract of dissertation, Voronezh (1965).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 21, No. 1, pp. 15–27, January–February, 1969.

The author is grateful to S. D. Éidel'naan for his interest in the investigation.

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Ivasishen, S.D. Estimates of Green's function of homogeneous first-boundary problem for a second-order parabolic equation in a noncylindrical region. Ukr Math J 21, 11–20 (1969). https://doi.org/10.1007/BF01086677

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  • DOI: https://doi.org/10.1007/BF01086677

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