TY - JOUR

T1 - Loaded differential equations and linear inverse problems for elliptic equations

AU - Kozhanov, A. I.

AU - Shipina, T. N.

N1 - Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - The article is devoted to the study of linear inverse problems of finding, alongside the solution, also the unknown right-hand side for second-order differential equations. The method of the study is based on reducing the initial inverse problems to direct, already nonlocal, boundary value problems for loaded (integro-differential) equations, proving the solvability of the new problems and then constructing solutions to the problems under study from the solutions to the new problems. The peculiarities of the inverse problems under study are new overdetermination conditions compared to the previous works. For the problems under study, we prove existence theorems for regular solutions (i.e. for solutions having all weak derivatives in the sense of Sobolev occurring in the equation). Some generalizations and strengthenings of the obtained results are given.

AB - The article is devoted to the study of linear inverse problems of finding, alongside the solution, also the unknown right-hand side for second-order differential equations. The method of the study is based on reducing the initial inverse problems to direct, already nonlocal, boundary value problems for loaded (integro-differential) equations, proving the solvability of the new problems and then constructing solutions to the problems under study from the solutions to the new problems. The peculiarities of the inverse problems under study are new overdetermination conditions compared to the previous works. For the problems under study, we prove existence theorems for regular solutions (i.e. for solutions having all weak derivatives in the sense of Sobolev occurring in the equation). Some generalizations and strengthenings of the obtained results are given.

KW - 35J25

KW - 35R30

KW - existence

KW - inverse problem

KW - loaded equation

KW - regular solution

KW - Second-order elliptic equation

KW - unknown right-hand side

UR - http://www.scopus.com/inward/record.url?scp=85089786393&partnerID=8YFLogxK

U2 - 10.1080/17476933.2020.1793970

DO - 10.1080/17476933.2020.1793970

M3 - Article

AN - SCOPUS:85089786393

VL - 66

SP - 910

EP - 928

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 6-7

ER -