Convergence of the solutions of a~nonlinear Dirichlet problem at the refinement of the boundary of the domain
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 236-250
Voir la notice de l'article provenant de la source Math-Net.Ru
This paper is devoted to the investigation of the convergence of the solutions of Dirichlet problems for quasilinear second-order elliptic equations in a sequence of domains $\Omega^s$ with a fine-grained boundary in the case of the concentration of the fine-grained boundary near some smooth surface. One indicates conditions under which the solutions of the investigated problems converge for $s\to\infty,$ one investigates the character of the convergence of the solutions, and one obtains a boundary problem for the limit function. It is shown that under certain conditions the solutions of the problems in the domains $\Omega^s$ can be replaced approximately, for large $s$, by the limit function which can be found without solving the sequence of problems in the domains $\Omega^s.$
@article{ZNSL_1982_115_a19,
author = {I. V. Skrypnik},
title = {Convergence of the solutions of a~nonlinear {Dirichlet} problem at the refinement of the boundary of the domain},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {236--250},
publisher = {mathdoc},
volume = {115},
year = {1982},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a19/}
}
TY - JOUR AU - I. V. Skrypnik TI - Convergence of the solutions of a~nonlinear Dirichlet problem at the refinement of the boundary of the domain JO - Zapiski Nauchnykh Seminarov POMI PY - 1982 SP - 236 EP - 250 VL - 115 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a19/ LA - ru ID - ZNSL_1982_115_a19 ER -
%0 Journal Article %A I. V. Skrypnik %T Convergence of the solutions of a~nonlinear Dirichlet problem at the refinement of the boundary of the domain %J Zapiski Nauchnykh Seminarov POMI %D 1982 %P 236-250 %V 115 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a19/ %G ru %F ZNSL_1982_115_a19
I. V. Skrypnik. Convergence of the solutions of a~nonlinear Dirichlet problem at the refinement of the boundary of the domain. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 236-250. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a19/