Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 114-125
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V. A. Kondrat'ev; O. A. Oleinik. Behavior of the generalized solutions of the Dirichlet problem for higher-order elliptic equations in the neighborhood of the boundary. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 114-125. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a9/
@article{ZNSL_1982_115_a9,
author = {V. A. Kondrat'ev and O. A. Oleinik},
title = {Behavior of the generalized solutions of the {Dirichlet} problem for higher-order elliptic equations in the neighborhood of the boundary},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {114--125},
year = {1982},
volume = {115},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a9/}
}
TY - JOUR
AU - V. A. Kondrat'ev
AU - O. A. Oleinik
TI - Behavior of the generalized solutions of the Dirichlet problem for higher-order elliptic equations in the neighborhood of the boundary
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1982
SP - 114
EP - 125
VL - 115
UR - http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a9/
LA - ru
ID - ZNSL_1982_115_a9
ER -
%0 Journal Article
%A V. A. Kondrat'ev
%A O. A. Oleinik
%T Behavior of the generalized solutions of the Dirichlet problem for higher-order elliptic equations in the neighborhood of the boundary
%J Zapiski Nauchnykh Seminarov POMI
%D 1982
%P 114-125
%V 115
%U http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a9/
%G ru
%F ZNSL_1982_115_a9
Making use of the method of weight functions and of energy inequalities, similar to the Saint-Venant principle, the authors obtain estimates which characterize the behavior of the generalized solutions of the Dirichlet problem for the general higher-order elliptic equation in the neighborhood of a boundary point. In the case of two independent variables one has obtained an estimate of the maximum of the modulus of the solution in the neighborhood of a boundary point.
