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On estimates of the fundamental solution of an elliptic equation with a small parameter
M. A. Evgrafov
Abstract:
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.
Received: 01.07.1980
Citation:
M. A. Evgrafov, “On estimates of the fundamental solution of an elliptic equation with a small parameter”, Mat. Sb. (N.S.), 116(158):1(9) (1981), 3–28; Math. USSR-Sb., 44:1 (1983), 1–22
Linking options:
https://www.mathnet.ru/eng/sm2430https://doi.org/10.1070/SM1983v044n01ABEH000949 https://www.mathnet.ru/eng/sm/v158/i1/p3
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Abstract page: | 295 | Russian version PDF: | 143 | English version PDF: | 3 | References: | 33 |
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