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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm3942https://doi.org/10.1070/SM2008v199n06ABEH003947 https://www.mathnet.ru/eng/sm/v199/i6/p137
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Abstract page: | 471 | Russian version PDF: | 221 | English version PDF: | 12 | References: | 60 | First page: | 5 |
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