Geodesic
On estimates of the fundamental solution of an elliptic equation with a~small parameter
Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 1-22

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The behavior of a fundamental solution $\Gamma(x,y;\varepsilon)$ of the elliptic equation $$ P\biggl(x,-i\varepsilon\,\frac\partial{\partial x}\biggr)u=0 $$ is studied for small $\varepsilon>0$ and fixed $x,y\in\mathbf R^n$. The main result is $$ \varlimsup_{\varepsilon\to+0}\varepsilon\ln|\Gamma(x,y;\varepsilon)|\leqslant-\rho_P(x,y), $$ where $\rho_P(x,y)$ is the distance between the points $x$ and $y$ in a Finsler metric connected with the function $P(x,\xi)$. Bibliography: 1 title. 
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     author = {M. A. Evgrafov},
     title = {On estimates of the fundamental solution of an elliptic equation with a~small parameter},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
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     number = {1},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_1_a0/}
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M. A. Evgrafov. On estimates of the fundamental solution of an elliptic equation with a~small parameter. Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 1-22. http://geodesic.mathdoc.fr/item/SM_1983_44_1_a0/