Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 1-22
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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/
@article{SM_1983_44_1_a0,
author = {M. A. Evgrafov},
title = {On estimates of the fundamental solution of an elliptic equation with a~small parameter},
journal = {Sbornik. Mathematics},
pages = {1--22},
year = {1983},
volume = {44},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1983_44_1_a0/}
}
TY - JOUR
AU - M. A. Evgrafov
TI - On estimates of the fundamental solution of an elliptic equation with a small parameter
JO - Sbornik. Mathematics
PY - 1983
SP - 1
EP - 22
VL - 44
IS - 1
UR - http://geodesic.mathdoc.fr/item/SM_1983_44_1_a0/
LA - en
ID - SM_1983_44_1_a0
ER -
%0 Journal Article
%A M. A. Evgrafov
%T On estimates of the fundamental solution of an elliptic equation with a small parameter
%J Sbornik. Mathematics
%D 1983
%P 1-22
%V 44
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1983_44_1_a0/
%G en
%F SM_1983_44_1_a0
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.
