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Inverse Source Problems
Preliminaries Results overlook Uniqueness theorems Singular points of the exterior potential Existence theory Parabolic problems Hyperbolic problems.
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Inverse problems for partial differential equations
Inverse Problems.- Ill-Posed Problems and Regularization.- Uniqueness and Stability in the Cauchy Problem.- Elliptic Equations: Single Boundary Measurements.- Elliptic Equations: Many BoundaryExpand
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On uniqueness in the inverse conductivity problem with local data
We show that the Dirichlet-to-Neumann map given on an arbitrary part of the boundary of a three-dimensional domain with zero Dirichlet (or Neumann) data on the remaining (spherical or plane) part ofExpand
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TOPICAL REVIEW: Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets
Market prices of financial derivatives such as options are directly observable. This information can be used to recover an unobservable local volatility function for the underlying stochasticExpand
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A nonhyperbolic cauchy problem for □b□c and its applications to elasticity theory
On etudie l'unicite et la stabilite d'une fonction u satisfaisant les conditions suivantes: □ b □ c u+A 3 u=f sur (−T,T)×G, (∂/∂N) j u=g j sur (−T,T)×Γ', j≤3, ou □ b u=bu tt −Δu, A k est un operateurExpand
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On uniqueness of recovery of a discontinuous conductivity coefficient
On considere le probleme de retrouver le coefficient a de l'equation elliptique div(a⊇u)=0 dans un domaine Ω avec la condition aux limites u=φ sur ∂Ω quand ∂u/∂N est donnee pour tout φ (regulier). OnExpand
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Stability estimates for hyperbolic inverse problems with local boundary data
The authors obtain stability estimates of recovery of two coefficients of a hyperbolic partial differential equation from all possible measurements implemented at a part of the lateral boundary.Expand
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Completeness of products of solutions and some inverse problems for PDE
Abstract In this paper we give conditions which guarantee that products of solutions of partial differential equations Pu + au = 0 are complete in L 2 (Ω) . Here P is a linear partial differentialExpand
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