On the problem of determining the parameter of an elliptic equation in a Banach space

Abstract

Abstract. The boundary value problem of determining the parameter of an elliptic equationwith a positive operator A in an arbitrary Banach space E is studied. The exact estimates are obtained for the solution of this problem in Hölder norms. Coercive stability estimates for the solution of boundary value problems for multi-dimensional elliptic equations are established.

Finite difference method for Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions

“…Abstract Theorems 2.4-2.6 permit us to get stable difference schemes for problem (3). We will discretize problem (3) in two steps.…”

“…Recent years, theory and methods of solving inverse problems of determining unknown parameter of differential equations have been comprehensively studied by several researchers (see [2-5, 11-21, 24-26, 28-30, 32] and the bibliography therein). The papers [3,[11][12][13][14][15][17][18][19] are devoted to study of well-posedness of various overdetermined problems for elliptic differential and difference equations. In [3,11,18,19], overdetermined problems with Dirichlet type overdetermination were investigated.…”

“…The papers [3,[11][12][13][14][15][17][18][19] are devoted to study of well-posedness of various overdetermined problems for elliptic differential and difference equations. In [3,11,18,19], overdetermined problems with Dirichlet type overdetermination were investigated. Inverse problems with Neumann type overdetermination were studied in papers [12,14,15].…”

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…Ashyralyev and Ashyralyyev study the BVP of determining the parameter of an elliptic equation in an arbitrary Banach space [6].…”

Stability of the space identification problem for the elliptic‐telegraph differential equation

“…Source identification problems for partial differential equations are used to model biological, physical, system engineering, and sociological processes and have been studied by many authors (see other studies [1][2][3][4][5][6][7][8][9][10][11][12] and the references given therein).…”