2014
DOI: 10.15388/na.2014.3.3
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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.

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Cited by 52 publications
(16 citation statements)
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“…Abstract Theorems 2.4-2.6 permit us to get stable difference schemes for problem (3). We will discretize problem (3) in two steps.…”
Section: A First and A Second Order Of Adss For Problem (3)mentioning
confidence: 99%
See 2 more Smart Citations
“…Abstract Theorems 2.4-2.6 permit us to get stable difference schemes for problem (3). We will discretize problem (3) in two steps.…”
Section: A First and A Second Order Of Adss For Problem (3)mentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
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“…Ashyralyev and Ashyralyyev study the BVP of determining the parameter of an elliptic equation in an arbitrary Banach space [6].…”
Section: Numerical Analysis For Boundary Value Problems With Nonlocalmentioning
confidence: 99%
“…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).…”
Section: Introductionmentioning
confidence: 99%