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Inverse problem for elliptic equation in a Banach space with Bitsadze–Samarsky boundary value conditions
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Dmitry G. Orlovsky
Veröffentlicht/Copyright:
1. Februar 2013
Abstract.
The two inverse problems of determining an unknown parameter in a nonhomogeneous part of the equation for an abstract second-order elliptic equation in a Banach space with boundary conditions of Bitsadze–Samarski type are considered. For the first problem we use the conditions of Dirichlet, and for the second problem we use the conditions of Neumann. Theorems of existence and uniqueness of solutions for both direct and inverse problems are proved. Explicit formulas for the solutions are obtained.
Keywords: Inverse problem; Banach space; semigroup; elliptic equation; Green's function; positive operator; operational calculus; characteristic function
Received: 2012-08-29
Published Online: 2013-02-01
Published in Print: 2013-02-01
© 2013 by Walter de Gruyter Berlin Boston
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Schlagwörter für diesen Artikel
Inverse problem;
Banach space;
semigroup;
elliptic equation;
Green's function;
positive operator;
operational calculus;
characteristic function
Artikel in diesem Heft
- Masthead
- Data regularization using Gaussian beams decomposition and sparse norms
- Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology
- The use of statistical tests to calibrate the normal SABR model
- Unique determination of potentials and semilinear terms of semilinear elliptic equations from partial Cauchy data
- Irregular nonlinear operator equations: Tikhonov's regularization and iterative approximation
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