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Sbornik: Mathematics, 2008, Volume 199, Issue 6, Pages 923–944
DOI: https://doi.org/10.1070/SM2008v199n06ABEH003947
(Mi sm3942)
 

This article is cited in 1 scientific paper (total in 1 paper)

Removable singularities for solutions of second-order linear uniformly elliptic equations in non-divergence form

A. V. Pokrovskii

Institute of Mathematics, Ukrainian National Academy of Sciences
References:
Abstract: Let $\mathfrak L$ be a linear uniformly elliptic operator of the second order in $\mathbb R^n$, $n\geqslant2$, with bounded measurable real coefficients, that satisfies the weak uniqueness property. The removability of compact subsets of a domain $D\subset\mathbb R^n$ is studied for weak solutions of the equation $\mathfrak Lf=0$ (in the sense of Krylov and Safonov) in some classes of continuous functions in $D$. In particular, a metric criterion for removability in Hölder classes with small exponent of smoothness is obtained.
Bibliography: 20 titles.
Received: 10.09.2007
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 6, Pages 137–160
DOI: https://doi.org/10.4213/sm3942
Bibliographic databases:
UDC: 517.956
MSC: 3560, 35J15
Language: English
Original paper language: Russian
Citation: A. V. Pokrovskii, “Removable singularities for solutions of second-order linear uniformly elliptic equations in non-divergence form”, Mat. Sb., 199:6 (2008), 137–160; Sb. Math., 199:6 (2008), 923–944
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm3942
  • https://doi.org/10.1070/SM2008v199n06ABEH003947
  • https://www.mathnet.ru/eng/sm/v199/i6/p137
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:471
    Russian version PDF:221
    English version PDF:12
    References:60
    First page:5
     
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