相关论文: Recovering nonsmooth coefficients for higher-order…

We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in $L^p$-based Sobolev spaces, $1<p<\infty$, of arbitrary smoothness $\ell$, is…

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…

We consider a linearized partial data Calder\'on problem for biharmonic operators extending the analogous result for harmonic operators. We construct special solutions and utilize Segal-Bargmann transform to recover lower order…

The inverse nodal problem for Dirac differential operator perturbated by a Volterra integral operator is studied. We prove that dense subset of the nodal points determines the coefficients of differential and integral part of the operator.…

This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…

Double forms are sections of the vector bundles $\Lambda^{k}T^*\mathcal{M}\otimes \Lambda^{m}T^*\mathcal{M}$, where in this work $(\mathcal{M},\mathfrak{g})$ is a compact Riemannian manifold with boundary. We study graded second-order…

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

In this paper, it is investigated for an inhomogeneous Dirichlet problem with $L^p$ boundary data for polyharmonic equation in the upper half-plane. By using higher order Poisson kernels and Pompeiu operators, which are respectively due to…

We study the existence and non-existence of classical solutions for inequalities of type $$ \pm \Delta^m u \geq \big(\Psi(|x|)*u^p\big)u^q \quad\mbox{ in } {\mathbb R}^N (N\geq 1). $$ Here, $\Delta^m$ $(m\geq 1)$ is the polyharmonic…

We prove two improved versions of the Hardy-Rellich inequality for the polyharmonic operator $(-\Delta)^m$ involving the distance to the boundary. The first involves an infinite series improvement using logarithmic functions, while the…

We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a…

In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability as an algebraic property implies that nonlinear maps are…

We consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator $\mathcal L_{g,X,q}$, with $X$ being a $W^{1,\infty}$ vector field and $q$ being an $L^\infty$ function on compact Riemannian…

In this paper, we introduce an inverse problem of a Schr\"odinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0<s<1$. We determine the unknown bounded potential $q$ from the exterior partial…

In this paper we establish commmutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in the upper half-space $\mathbb{R}^{n+1}_+:=\{(x,t)\in \mathbb{R}^n \times (0,\infty)\}$, with uniformly…

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…

We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neumann map. By applying higher order linearization method, we…

We study inverse boundary problems for third-order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in $\mathbb{R}^n$, where $n\geq 3$. By imposing appropriate assumptions on the nonlinearity, we demonstrate…