Geodesic
Estimates of $C^m$-Capacity of Compact Sets in $\mathbb{R}^N$
Matematičeskie zametki, Tome 75 (2004) no. 6, pp. 803-817

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For a given homogeneous elliptic partial differential operator $L$ with constant complex coefficients, the Banach space $V$ of distributions in $\mathbb{R}^N$ and a compact set $X$ in $\mathbb{R}^N$, we study the quantity $\lambda_{V,L}(X)$ equal to the distance in $V$ from the class of functions $f_0$ satisfying the equation $Lf_0 = 1$ in a neighborhood of $X$ (depending on $f_0$) to the solution space of the equation $Lf= 0$ in the neighborhoods of $X$. For $V=BC^m$, we obtain upper and lower bounds for $\lambda_{V,L}(X)$ in terms of the metric properties of the set $X$, which allows us to obtain estimates for $\lambda_{V,L}(X)$ for a wide class of spaces $V$. 
@article{MZM_2004_75_6_a0,
     author = {A. M. Voroncov},
     title = {Estimates of $C^m${-Capacity} of {Compact} {Sets} in $\mathbb{R}^N$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--817},
     publisher = {mathdoc},
     volume = {75},
     number = {6},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a0/}
}
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A. M. Voroncov. Estimates of $C^m$-Capacity of Compact Sets in $\mathbb{R}^N$. Matematičeskie zametki, Tome 75 (2004) no. 6, pp. 803-817. http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a0/