Related papers: On Single Measurement Stability for the Fractional…
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly…
We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in $\mathbb{R}^2$. The obstacle is of general polygonal shape and the impedance parameter can be variable. We establish the stability results by…
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…
In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these…
We study the stability properties of periodic solutions to the Nonlinear Schr\"odinger (NLS) equation with a periodic potential. We exploit the symmetries of the problem, in particular the Hamiltonian structure and the $\U(1)$ symmetry. We…
This article deals with the weak and strong unique continuation principle for fractional Schr\"odinger equations with scaling-critical and rough potentials via Carleman estimates. Our methods allow to apply the results to variable…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
The main goal of this paper is to present orbital stability results of periodic standing waves for the one-dimensional logarithmic Klein-Gordon equation. To do so, we first use compactness arguments and a non-standard analysis to obtain the…
The purpose of this article is to extend the uniqueness results for the two dimensional Calder\'on problem to unbounded potentials on general geometric settings. We prove that the Cauchy data sets for Schr\"odinger equations uniquely…
This article is concerned with the mathematical analysis of a class of a nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We prove existence and uniqueness of global-in-time solutions to the associated…
In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…
We prove uniqueness of solutions to the Cauchy problem for the derivative nonlinear Schr\"odinger equation in $L^\infty_tH^{1/2}_x$. Our proof is based on the method of normal form reduction (NFR), which has been employed to obtain the…
For the one-dimensional mass-critical/supercritical pseudo-relativistic nonlinear Schrodinger equation, a stationary solution can be constructed as an energy minimizer under an additional kinetic energy constraint and the set of energy…
The manuscript is concerned with uniqueness and stability for inverse source problem of determining spatially varying factor $f(x)$ of a source term given by $R(t)f(x)$ with suitable given $R(t)$ in the right hand side of the Schr\"odinger…
In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on…
We introduce the boundary measure at scale r of a compact subset of the n-dimensional Euclidean space. We show how it can be computed for point clouds and suggest these measures can be used for feature detection. The main contribution of…
In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and…
We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calder\'on-Zygmund type estimates of $u/d^s$ depending on the regularity…
We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based…
In this paper, the space-fractional Schr\"{o}dinger equations with singular potentials are studied. Delta-like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of 'weakened'…