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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 2, Pages 44–55 (Mi faa2901)  

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

Removable Singularities of Solutions of Linear Uniformly Elliptic Second Order 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 real coefficients in a bounded domain $G\subset\mathbb{R}^n$ ($n\ge 2$). We define classes of continuous functions in $G$ that contain generalized solutions of the equation $Lf=0$ and have the property that the compact sets removable for such solutions in these classes can be completely described in terms of Hausdorff measures.

Keywords: removable singularity, elliptic operator, generalized solution, Green function, Hausdorff measure

DOI: https://doi.org/10.4213/faa2901

Full text: PDF file (218 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:2, 116–125

Bibliographic databases:

UDC: 517.956
Received: 15.09.2006

Citation: A. V. Pokrovskii, “Removable Singularities of Solutions of Linear Uniformly Elliptic Second Order Equations”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 44–55; Funct. Anal. Appl., 42:2 (2008), 116–125

Citation in format AMSBIB
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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, “Removable singularities for solutions of second-order linear uniformly elliptic equations in non-divergence form”, Sb. Math., 199:6 (2008), 923–944  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. N. Kondrashov, “On the asymptotics of solutions of elliptic equations at the ends of non-compact Riemannian manifolds with metrics of a special form”, Izv. Math., 83:2 (2019), 287–314  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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