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Mat. Zametki, 2003, Volume 74, Issue 5, Pages 676–685 (Mi mz300)  

This article is cited in 5 scientific papers (total in 5 papers)

Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes

A. A. Kovalevsky

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: We establish the existence of a weak solution to the Dirichlet problem belonging to a Sobolev space for nonlinear elliptic equations of second order with right-hand sides from a wide class of functions defined in terms of the logarithmic function.

DOI: https://doi.org/10.4213/mzm300

Full text: PDF file (212 kB)
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English version:
Mathematical Notes, 2003, 74:5, 637–646

Bibliographic databases:

UDC: 517.9
Received: 22.06.2001
Revised: 08.04.2002

Citation: A. A. Kovalevsky, “Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes”, Mat. Zametki, 74:5 (2003), 676–685; Math. Notes, 74:5 (2003), 637–646

Citation in format AMSBIB
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\pages 676--685
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\jour Math. Notes
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\pages 637--646
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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. A. A. Kovalevsky, “A priori properties of solutions of nonlinear equations with degenerate coercivity and $L^1$-data”, Journal of Mathematical Sciences, 149:5 (2008), 1517–1538  mathnet  crossref  mathscinet
    2. Kovalevsky, AA, “General conditions for limit summability of solutions of nonlinear elliptic equations with L-1-data”, Nonlinear Analysis-Theory Methods & Applications, 64:8 (2006), 1885  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Kovalevsky A.A., Nicolosi F., “On limit summability of solutions for a class of degenerate nonlinear high-order equations with L-1-data”, Complex Variables and Elliptic Equations, 55:11 (2010), 1047–1058  crossref  mathscinet  zmath  isi  scopus  scopus
    4. A. A. Kovalevsky, Yu. S. Gorban, “On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data”, Izv. Math., 75:1 (2011), 101–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. A. A. Kovalevsky, “Summability of Solutions of the Dirichlet Problem for Nonlinear Elliptic Equations with Right-Hand Side in Classes Close to $L^1$”, Math. Notes, 107:6 (2020), 993–998  mathnet  crossref  crossref  isi  elib
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