Related papers: An inverse problem for the p-Laplacian: boundary d…
For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…
We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications…
We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function.…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in…
We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of…
We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a…
We study inverse conductivity problem for an anisotropic conductivity in $L^\infty$ in bounded and unbounded domains. Also, we give applications of the results in the case when Dirichlet-to-Neumann and Neumann-to-Dirichlet maps are given…
We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
We study the isotropic elastic wave equation in a bounded domain with boundary. We show that local knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the p-wave locally if there is a strictly convex foliation with…
We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the…
In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient in the wave equation with Dirichlet data from measured Neumann boundary observations. This…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…
We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…
We study the solvability of $(p,q)$-Laplacian problems with nonlinear reaction terms and non-homogeneous Neumann boundary conditions. First, we provide a complete description of the spectrum of the eigenvalue problem involving the…
We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is…
We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by the Maxwell equations. Both of the systems are controlled from…