Proof of uniqueness and membership in $W^1_2$ of the classical solution of a mixed problem for a self-adjoint hyperbolic equation
Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 91-101
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In this article a uniqueness theorem for the classical solution of a mixed problem is proved under minimal assumptions on the coefficients of the differential operator for admitting the Fourier method of a hyperbolic second-order equation in an $(N+1)$-dimensional cylinder, whose cross section is a completely arbitrary bounded $N$-dimensional domain. Furthermore, it is proved that the classical solution of the indicated mixed problem, whenever it exists, belongs to the class $W^1_2$ and is the generalized solution from $W^1_2$ of the same problem.
@article{MZM_1975_17_1_a10,
author = {V. A. Il'in},
title = {Proof of uniqueness and membership in $W^1_2$ of the classical solution of a mixed problem for a self-adjoint hyperbolic equation},
journal = {Matemati\v{c}eskie zametki},
pages = {91--101},
year = {1975},
volume = {17},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a10/}
}
TY - JOUR AU - V. A. Il'in TI - Proof of uniqueness and membership in $W^1_2$ of the classical solution of a mixed problem for a self-adjoint hyperbolic equation JO - Matematičeskie zametki PY - 1975 SP - 91 EP - 101 VL - 17 IS - 1 UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a10/ LA - ru ID - MZM_1975_17_1_a10 ER -
%0 Journal Article %A V. A. Il'in %T Proof of uniqueness and membership in $W^1_2$ of the classical solution of a mixed problem for a self-adjoint hyperbolic equation %J Matematičeskie zametki %D 1975 %P 91-101 %V 17 %N 1 %U http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a10/ %G ru %F MZM_1975_17_1_a10
V. A. Il'in. Proof of uniqueness and membership in $W^1_2$ of the classical solution of a mixed problem for a self-adjoint hyperbolic equation. Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 91-101. http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a10/