Geodesic
Removable Singularities of Solutions of Linear Uniformly Elliptic Second Order Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 2, pp. 44-55

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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. 
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     author = {A. V. Pokrovskii},
     title = {Removable {Singularities} of {Solutions} of {Linear} {Uniformly} {Elliptic} {Second} {Order} {Equations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {44--55},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_2_a5/}
}
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A. V. Pokrovskii. Removable Singularities of Solutions of Linear Uniformly Elliptic Second Order Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 2, pp. 44-55. http://geodesic.mathdoc.fr/item/FAA_2008_42_2_a5/