2023; Physical and Mathematical Sciences, 57(2 (261): 44–50
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ON CORRECT SOLVABILITY OF DIRICHLET PROBLEM IN A HALF-SPACE FOR REGULAR EQUATIONS WITH NON-HOMOGENEOUS BOUNDARY CONDITIONS

Mikayel Khachaturyan*

Received: 2025-01-21 · Published: 2023-06-22

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CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON CORRECT SOLVABILITY OF DIRICHLET PROBLEM IN A HALF-SPACE FOR REGULAR EQUATIONS WITH NON-HOMOGENEOUS BOUNDARY CONDITIONS
Author
Mikayel Khachaturyan
Published
2023-06-22
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2023.57.2.044

Abstract

In this paper we consider the following Dirichlet problem with non-homogeneous boundary conditions in a multianisotropic Sobolev space W2M(R2×R+){P(Dx,Dx3)u=f(x,x3),x3>0,x∈R2,Dx3su|x3=0=φs(x),s=0,…,m−1.It is assumed that P(Dx,Dx3) is a multianisotopic regular operator of a special form with a characteristic polyhedron M. We prove unique solvability of the problem in the space W2M(R2×R+), assuming additionally, that f(x,x3) belongs to L2(R2×R+) and has a compact support, boundary functions φs belong to special Sobolev spaces of fractional order and have compact supports.
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