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We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schr\"odinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when…

Analysis of PDEs · Mathematics 2013-09-12 Victor Isakov , Jenn-Nan Wang

In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…

Analysis of PDEs · Mathematics 2014-07-03 Sergio Vessella

We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This estimate is proved under the assumption that the potential…

Analysis of PDEs · Mathematics 2026-01-21 Mourad Choulli , Hiroshi Takase

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…

Analysis of PDEs · Mathematics 2015-05-04 Ru-Yu Lai , Victor Isakov , Jenn-Nan Wang

We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

Analysis of PDEs · Mathematics 2024-03-21 Tianjiao Wang , Xiang Xu , Yue Zhao

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schr\"{o}dinger equation. The rigorous justification of increasing stability for the IBVP for Schr\"{o}dinger equation were…

Analysis of PDEs · Mathematics 2023-01-13 Pu-Zhao Kow , Gunther Uhlmann , Jenn-Nan Wang

This paper concerns inverse problems for strongly coupled Schr\"odinger equations. The purpose of this inverse problem is to retrieve a stationary potential in the strongly coupled Schr\"odinger equations from either boundary or internal…

Analysis of PDEs · Mathematics 2020-12-09 Xiaomin Zhu , Fangfang Dou

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are…

Analysis of PDEs · Mathematics 2022-04-27 Shuai Lu , Mikko Salo , Boxi Xu

We investigate recovery of the (Schr\"odinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a H\"older type stability which is a big improvement over a…

Analysis of PDEs · Mathematics 2020-08-19 Victor Isakov , Shuai Lu , Boxi Xu

This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…

Analysis of PDEs · Mathematics 2025-12-29 Tianjiao Wang , Xiang Xu , Yue Zhao

We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.

Analysis of PDEs · Mathematics 2013-06-27 Mikhail Isaev

We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

Analysis of PDEs · Mathematics 2007-12-07 Roman Novikov

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is…

Analysis of PDEs · Mathematics 2020-09-29 L. Potenciano-Machado , A. Ruiz , L. Tzou

In this paper, we establish the existence of ground state solutions for a fractional Schr\"odinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide…

Analysis of PDEs · Mathematics 2025-03-07 Zhiyan Ding , Hichem Hajaiej

We give stability estimates in the Cauchy problem for general partial differential equation of the elliptic type similar to the Helmholtz equation. We do not impose any (pseudo)convexity assumptions on the domain or the operator. These…

Analysis of PDEs · Mathematics 2018-07-04 Victor Isakov

In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…

Analysis of PDEs · Mathematics 2022-11-08 Xiaomeng Zhao , Ganghua Yuan

In this paper we study local stability estimates for a magnetic Schr\"odinger operator with partial data on an open bounded set in dimension $n\geq 3$. This is the corresponding stability estimates for the identifiability result obtained by…

Analysis of PDEs · Mathematics 2017-09-13 Leyter Potenciano-Machado

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…

Analysis of PDEs · Mathematics 2015-09-02 Fikret Gölgeleyen , Masahiro Yamamoto