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Inverse Problems for Elliptic Equations
2017This chapter is an introduction to the basic inverse problems for elliptic equations. One class of these inverse problems arises when the Born approximation is used for scattering problem in quantum mechanics, acoustics or electrodynamics. In the first part of this chapter two inverse problems, the inverse scattering problem at a fixed energy and the ...
Alemdar Hasanov Hasanoğlu +1 more
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Stability estimates for an inverse elliptic problem
jiip, 2002Abstract - We prove stability estimates for an inverse elliptic problem consisting in the determination of an unknown boundary coefficient from an overdetermined data. We consider both the case of all boundary measurements and the case of single boundary measurement.
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On approximation of inverse problems for abstract elliptic problems
Journal of Inverse and Ill-posed Problems, 2009The authors consider an inverse problem of an abstract elliptic differential equation with respect to a general Banach space. The problem is overdetermined and thus an operator-valued source term has to be identified such that a solution exists. The authors investigate two scenarios.
Orlovsky, D., Piskarev, S.
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Nonlinear inverse problems for elliptic equations
jiip, 2001Abstract - In this paper we prove the existence of regular solutions for some nonlinear coefficient inverse problems for elliptic equations.
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Stability estimate for a semilinear elliptic inverse problem
Nonlinear Differential Equations and Applications NoDEA, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mourad Choulli +2 more
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Some inverse problems for elliptic equations
Applicable Analysis, 1988We examine the question of identifying certain coefficients in elliptic equations from overposed boundary data . These coefficients have a known value in a subset of the domain, and another known value on its complement; the problem is to identify this ...
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On Elliptic Inverse Heat Conduction Problems
Journal of Heat Transfer, 2017This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed ...
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Inverse coefficient problems for elliptic hemivariational inequalities
Chinese Annals of Mathematics, Series B, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao, Cui'e, Liu, Zhenhai
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Numerical methods for elliptic inverse problems
International Journal of Computer Mathematics, 1998Identifying physical parameters in elliptic boundary value problems is formulated as a constrained minimization problem using the output least squares method with the H l-regularization or the BV-regularization. The constrained minimization problem is then discretized by finite element methods and the discretization is shown to be convergent for both ...
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Inverse problems for elliptic equations in the space: II
Differential Equations, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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