Search Results - Boundary value AND inverse problems for harmonic functions in two dimensions

A density property for tensor products of gradients of harmonic functions and applications by Cârstea, Cătălin I., Feizmohammadi, Ali

“… We then demonstrate the usefulness of this result by using it to prove uniqueness in the inverse boundary value problem for a coupled quasilinear elliptic system…”
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Geometric Aspects of Shape Optimization by Plotnikov, Pavel I., Sokolowski, Jan

“… Shape optimization is a part of calculus of variations which uses the geometry. Shape optimization is also related to the free boundary problems in the theory of Partial Differential Equations…”
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Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions by Mitrea, Irina

“… < ∞, on curvilinear polygons. Furthermore, we produce norm estimates/formulas for inverses of singular integral operators relevant for the Dirichlet, Neumann, tangential derivative, and transmission boundary value problems…”
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Elliptic partial differential equations and quasiconformal mappings in the plane (princeton mathematical series) by Astala, Kari, Iwaniec, Tadeusz, Martin, Gaven

“…: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations…”
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Gradient-Based Quantitative Image Reconstruction in Ultrasound-Modulated Optical Tomography: First Harmonic Measurement Type in a Linearised Diffusion Formulation by Powell, Samuel, Arridge, Simon R., Leung, Terence S.

“… on the boundary of a given domain. We derive and examine the correlation measurement density functions of the model which describe the sensitivity of the modality to perturbations in the optical parameters of interest…”
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A moving pseudo-boundary method of fundamental solutions for void detection by Karageorghis, Andreas, Lesnic, Daniel, Marin, Liviu

“… This problem can be modeled as an inverse boundary value problem for harmonic functions. The algorithm for imaging the interior of the medium also makes use of radial polar parametrization of the unknown void shape in two dimensions…”
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Acoustic Scattering by Mildly Rough Unbounded Surfaces in Three Dimensions by Chandler-Wilde, Simon N., Eric Heinemeyer, Potthast, Roland

“…For a nonlocally perturbed half-space we consider the scattering of time-harmonic acoustic waves…”
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A density property for tensor products of gradients of harmonic functions and applications by Cârstea, Cătălin I, Feizmohammadi, Ali

“… We then demonstrate the usefulness of this result by using it to prove uniqueness in the inverse boundary value problem for a coupled quasilinear elliptic system…”
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A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains by Yao, Jianan, Xie, Baoling, Lai, Jun

“… In this paper, we focus on the efficient and high-precision numerical algorithm for the time harmonic elastic wave scattering problems from cornered domains via the boundary integral equations in two dimensions…”
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Interior Backus Problem with Expanded Data by Zheng, Yuxiang

“…We consider a special formulation of the Backus geomagnetic problem in two and higher dimension. Given a domain Ω…”
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On the Far Field Patterns for Electromagnetic Scattering in Two Dimensions by Athanasiadis, Christodoulos E., Athanasiadou, Evagelia S., Roupa, Paraskevi

“… The corresponding scattering problems are reduced to mixed boundary value problems for the two-dimensional Helmholtz equation…”
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Detection of cavities using the method of fundamental solutions by Karageorghis, A., Lesnic, D.

“… boundary of the medium, can be modelled as an inverse boundary value problem for harmonic functions…”
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One problem on generating 2D regular grids based on mappings by Azarenok, B. N., Charakhch’yan, A. A.

“… for the inverse harmonic mapping of the unit square onto the domain with a certain mapping of the domain boundaries is developed…”
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