The structure of fractional spaces generated by the two-dimensional difference operator on the half plane
We consider a difference operator approximation $A^x_h$ of the differential operator $A^xu(x) = a_{11}(x)u_{x_1 x_1}(x) - a_{22}(x)u_{x_2x_2} (x) + \sigma u(x),\; x = (x_1, x_2)$ defined in the region $R^{+} \times R$ with the boundary condition $u(0, x_2) = 0,\; x_2 \in R$. Here, the coefficients...
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| Date: | 2018 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1614 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider a difference operator approximation $A^x_h$ of the differential operator $A^xu(x) = a_{11}(x)u_{x_1 x_1}(x) - a_{22}(x)u_{x_2x_2} (x) + \sigma u(x),\; x = (x_1, x_2)$ defined in the region $R^{+} \times R$ with the boundary condition $u(0, x_2) = 0,\; x_2 \in R$. Here, the coefficients $a_{ii}(x), i = 1, 2$, are continuously differentiable, satisfy the uniform ellipticity condition
$a^2_{11}(x) + a^2_{22}(x) \geq \delta > 0$. We investigate the structure of the fractional spaces generated by the
analyzed difference operator. Theorems on well-posedness in a Holder space of difference elliptic problems are obtained
as applications. |
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