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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 1(9), Pages 3–28 (Mi msb2430)  

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
$$ P(x,-i\varepsilon \frac\partial{\partial x})u=0 $$
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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English version:
Mathematics of the USSR-Sbornik, 1983, 44:1, 1–22

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J30, 35B45; Secondary 35E05
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

Citation in format AMSBIB
\Bibitem{Evg81}
\by M.~A.~Evgrafov
\paper On estimates of the fundamental solution of an elliptic equation with a~small parameter
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 1(9)
\pages 3--28
\mathnet{http://mi.mathnet.ru/msb2430}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=632487}
\zmath{https://zbmath.org/?q=an:0494.35006|0471.35005}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 1
\pages 1--22
\crossref{https://doi.org/10.1070/SM1983v044n01ABEH000949}


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