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Mat. Sb., 2009, Volume 200, Number 10, Pages 3–24 (Mi msb7477)  

This article is cited in 2 scientific papers (total in 2 papers)

Elliptic and parabolic inequalities with point singularities on the boundary

E. I. Galakhov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is shown that various quasilinear elliptic and parabolic differential inequalities and systems of such inequalities defined on bounded domains, and which have point singularities on the boundary do not have solutions. The method of nonlinear capacity is used in the proof. Examples show that the conditions obtained by this method cannot be improved in the class of problems under consideration.
Bibliography: 14 titles.

Keywords: quasilinear equations, nonexistence of solutions, boundary singularities.

DOI: https://doi.org/10.4213/sm7477

Full text: PDF file (561 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:10, 1417–1437

Bibliographic databases:

UDC: 517.954
MSC: Primary 35R45; Secondary 36A20
Received: 29.10.2008 and 08.05.2009

Citation: E. I. Galakhov, “Elliptic and parabolic inequalities with point singularities on the boundary”, Mat. Sb., 200:10 (2009), 3–24; Sb. Math., 200:10 (2009), 1417–1437

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7477
  • http://mi.mathnet.ru/eng/msb/v200/i10/p3

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. I. Galakhov, “On higher order elliptic and parabolic inequalities with singularities on the boundary”, Proc. Steklov Inst. Math., 269 (2010), 76–84  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Galakhov E.I., “On the Solvability of Nonlinear Differential Inequalities with Singular Coefficients”, Differ. Equ., 49:1 (2013), 45–58  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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