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Sbornik: Mathematics, 2004, Volume 195, Issue 11, Pages 1607–1638
DOI: https://doi.org/10.1070/SM2004v195n11ABEH000859 (Mi sm859) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Singular solutions of higher-order non-linear elliptic systems

E. A. Kalita

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
English version PDF (322 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2004v195n11ABEH000859
Abstract: The behaviour of solutions of non-linear elliptic systems is studied in the neighbourhood of a singular point, finite or infinite. It is shown that if the order of the singularity lies in a certain interval depending on the modulus of ellipticity of the system, then it is equal to the order of the singularity of some singular solution for the poly-Laplacian operator. Sharp two-sided energy estimates in the neighbourhood of the singular point are obtained for such solutions. Global solutions are considered, for which lower energy bounds are derived from upper estimates. Counterexamples constructed for second-order equations and systems demonstrate that the interval of regular behaviour of the order of the singularity is precisely described.
Received: 06.06.2003
Russian version:
Matematicheskii Sbornik, 2004, Volume 195, Number 11, Pages 63–94
DOI: https://doi.org/10.4213/sm859
Bibliographic databases:
UDC: 517.956
MSC: 35B05, 35J30, 35J45
Language: English
Original paper language: Russian
Citation: E. A. Kalita, “Singular solutions of higher-order non-linear elliptic systems”, Mat. Sb., 195:11 (2004), 63–94; Sb. Math., 195:11 (2004), 1607–1638
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    English version PDF:6
    References:55
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