相关论文: Two uniqueness results in the inverse boundary val…

We consider inverse boundary value problems for the Navier-Stokes equations and the isotropic Lam\'e system in two dimensions. The uniqueness without any smallness assumptions on unknown coefficients, which is called global uniqueness, was…

We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ \epsilon(x)\partial_t u^m-\nabla\cdot\bigl(\gamma(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{in }(0,T)\times\Omega, \] where…

We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness…

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…

In this paper we consider the inverse boundary value problem for the Schr\"odinger equation with potential in $L^p$ class, $p>4/3$. We show that the potential is uniquely determined by the boundary measurements.

We give a uniqueness result in dimension 2 for the solutions to an equation on compact Riemannian surface without boundary.

We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…

We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…

We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…

Two main results are presented: 1) a new class of applied problems that lead to equations with $(p,q)$-Laplace is presented; 2) a method for solving nonlinear boundary value problems involving $(p,q)$-Laplace with measurable unbounded…

We consider weighted p-Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp…

In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the…

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…

In this paper we prove the~existence of two non-trivial weak solutions of Dirichlet boundary value problem for p-Laplacian problem with a~singular part and two disturbances satisfying the~proper assumptions. The~abstract existence result we…

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-\'Emery Laplacian $-\Delta_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary…