☆ 4.5 Article

REMARKS ON THE ANISOTROPIC CALDERON PROBLEM

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2023)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Mathematics

Inverse problems for elliptic equations with fractional power type nonlinearities

Tony Liimatainen et al.

Summary: This study focuses on inverse problems for semilinear elliptic equations with fractional power type nonlinearities. By utilizing a higher order linearization method and a fractional order adaptation, the general power type nonlinearities remain valid for the results from previous research.

JOURNAL OF DIFFERENTIAL EQUATIONS (2022)

添加到收藏夹

Article Mathematics

Linearized Calderon problem and exponentially accurate quasimodes for analytic manifolds

Katya Krupchyk et al.

Summary: In this article, we study the linearized anisotropic Calderon problem on a compact Riemannian manifold with boundary. By solving the problem under certain geometric conditions, it is shown that products of pairs of harmonic functions on the manifold form a complete set.

ADVANCES IN MATHEMATICS (2022)

添加到收藏夹

Article Mathematics, Applied

Inverse problems for elliptic equations with power type nonlinearities

Matti Lassas et al.

Summary: The method introduced is for solving Calderon type inverse problems for semilinear equations with power type nonlinearities, using higher order linearizations for cases where the solution for a corresponding linear equation is unknown. Assuming knowledge of a nonlinear Dirichlet-to-Neumann map, it can determine both a potential and a conformal manifold simultaneously in dimension 2, and a potential on transversally anisotropic manifolds in dimensions n >= 3. In the Euclidean case, the Calderon problem for certain semilinear equations can be solved in a surprisingly simple way without using complex geometrical optics solutions.

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES (2021)

添加到收藏夹

Article Mathematics

Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations

Matti Lassas et al.

Summary: The study focuses on various partial data inverse boundary value problems for the semilinear elliptic equation using higher order linearization technique. The Dirichlet-to-Neumann map is shown to determine the Taylor series of a(x, z) at z=0, while simultaneously detecting unknown cavities or parts of the boundary. The method relies on the solution of linearized partial data Calderon problem and has implications for certain semilinear equations as well.

REVISTA MATEMATICA IBEROAMERICANA (2021)

添加到收藏夹

Article Mathematics

Reconstruction in the Calderon problem on conformally transversally anisotropic manifolds

Ali Feizmohammadi et al.

Summary: This study demonstrates the constructive determination of a continuous potential on a conformally transversally anisotropic manifold using the Dirichlet-to-Neumann map for the Schrodinger operator, assuming the geodesic ray transform on the transversal manifold is constructively invertible. The reconstruction process relies on complex geometric optics solutions based on Gaussian beams quasimodes concentrated along non-tangential geodesics. Additionally, a reconstruction formula for the boundary trace of a continuous potential is derived from the knowledge of the Dirichlet-to-Neumann map.

JOURNAL OF FUNCTIONAL ANALYSIS (2021)

添加到收藏夹

Article Mathematics

The Poisson embedding approach to the Calderon problem

Matti Lassas et al.

MATHEMATISCHE ANNALEN (2020)

添加到收藏夹

Article Mathematics

The Linearized Calderon Problem in Transversally Anisotropic Geometries

David Dos Santos Ferreira et al.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2020)

添加到收藏夹

Article Mathematics, Applied

A REMARK ON PARTIAL DATA INVERSE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATIONS

Katya Krupchyk et al.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2020)

添加到收藏夹

Article Mathematics

An inverse problem for a semi-linear elliptic equation in Riemannian geometries

Ali Feizmohammadi et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2020)

添加到收藏夹

Proceedings Paper Mathematics

Multidimensional Borg-Levinson inverse spectral problems

Eric Soccorsi

IDENTIFICATION AND CONTROL: SOME NEW CHALLENGES (2020)

添加到收藏夹

Article Mathematics

Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations

Yaroslav Kurylev et al.

INVENTIONES MATHEMATICAE (2018)

添加到收藏夹

Article Mathematics, Applied

The Calderon problem in transversally anisotropic geometries

David Dos Santos Ferreira et al.

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2016)

添加到收藏夹

Article Mathematics

Inverse problems: seeing the unseen

Gunther Uhlmann

BULLETIN OF MATHEMATICAL SCIENCES (2014)

添加到收藏夹

Article Mathematics

Limiting Carleman weights and anisotropic inverse problems

David Dos Santos Ferreira et al.

INVENTIONES MATHEMATICAE (2009)

添加到收藏夹

Article Mathematics, Applied

INVERSE PROBLEMS FOR EINSTEIN MANIFOLDS

Colin Guillarmou et al.

INVERSE PROBLEMS AND IMAGING (2009)

添加到收藏夹

Article Mathematics, Applied

Equivalence of time-domain inverse problems and boundary spectral problems

A Katchalov et al.

INVERSE PROBLEMS (2004)

添加到收藏夹

Article Mathematics, Applied

Inverse boundary value problems for a class of semilinear elliptic equations

ZQ Sun

ADVANCES IN APPLIED MATHEMATICS (2004)

添加到收藏夹

Article Mathematics

On determining a Riemannian manifold from the Dirichlet-to-Neumann map

M Lassas et al.

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE (2001)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.