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Mat. Zametki, 2005, Volume 77, Issue 3, Pages 424–433 (Mi mz2503)  

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

Removable singularities of solutions of second-order divergence-form elliptic equations

A. V. Pokrovskii

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Let $L$ be a uniformly elliptic linear second-order differential operator in divergence form with bounded measurable coefficients in a bounded domain $G\subset\mathbb R^n$ $(n\geqslant2)$. In this paper, we introduce subclasses of the Sobolev class $W^{1,2}(G)_{loc}$ containing generalized solutions of the equation $Lu=0$ such that the closed sets of nonisolated removable singular points for such solutions can be described completely in terms of Hausdorff measures.

DOI: https://doi.org/10.4213/mzm2503

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English version:
Mathematical Notes, 2005, 77:3, 391–399

Bibliographic databases:

UDC: 517.956
Received: 17.10.2003

Citation: A. V. Pokrovskii, “Removable singularities of solutions of second-order divergence-form elliptic equations”, Mat. Zametki, 77:3 (2005), 424–433; Math. Notes, 77:3 (2005), 391–399

Citation in format AMSBIB
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\paper Removable singularities of solutions of second-order divergence-form elliptic equations
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\yr 2005
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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. A. V. Pokrovskii, “Local approximations by solutions of second-order elliptic equations and removable singularities”, Doklady Mathematics, 76:3 (2007), 921–924  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. V. Pokrovskii, “Removable Singularities of Solutions of Linear Uniformly Elliptic Second Order Equations”, Funct. Anal. Appl., 42:2 (2008), 116–125  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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