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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 1, Pages 53–70 (Mi izv3292)  

This article is cited in 3 scientific papers (total in 3 papers)

On the decay of solutions of non-uniformly elliptic equations

V. F. Gilimshina, F. Kh. Mukminov

Bashkir State Pedagogical University

Abstract: We obtain upper and lower bounds for the rate of decay at infinity for a solution of a second-order non-uniformly elliptic equation in an unbounded domain with alternating types of boundary condition, both of the first and third types. We prove that the bound for this rate of decay is sharp, both in the case of a rather arbitrary alternation of boundary conditions of the first and third types and in the case of an equation degenerating on the boundary of an unbounded domain.

Keywords: degenerate elliptic equation, rate of decay of solutions, unbounded domain.

DOI: https://doi.org/10.4213/im3292

Full text: PDF file (580 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:1, 53–71

Bibliographic databases:

UDC: 517.94
MSC: Primary 35J25; Secondary 35H99, 35J70
Received: 28.07.2008

Citation: V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. RAN. Ser. Mat., 75:1 (2011), 53–70; Izv. Math., 75:1 (2011), 53–71

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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. D. O. Degtyarev, A. M. Il'in, “The asymptotics of a solution of a parabolic equation as time increases without bound”, Sb. Math., 203:11 (2012), 1589–1610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Yu. A. Alkhutov, V. N. Denisov, “Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero”, Trans. Moscow Math. Soc., 75 (2014), 233–258  mathnet  crossref  elib
    3. L. M. Kozhevnikova, A. A. Khadzhi, “O resheniyakh ellipticheskikh uravnenii s nestepennymi nelineinostyami v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 44–62  mathnet  crossref  zmath  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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