相关论文: A straightforward proof of Carleman estimate for s…

In this paper, we derive a local Carleman estimate for the complex second order elliptic operator with Lipschitz coefficients having jump discontinuities. Combing the result in [BL] and the arguments in [DcFLVW], we present an elementary…

We prove a Carleman estimate for elliptic second order partial differential operators with Lipschitz continuous coefficients. The Carleman estimate is valid for any complex-valued function $u\in W^{2,2}$ with support in a punctured ball of…

We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation…

In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. Our approach does not rely on the techniques of microlocal analysis. We…

By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have…

This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then…

In this paper we study the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a…

In this paper, we would like to derive three-ball inequalities and propagation of smallness for the complex second order elliptic equation with discontinuous Lipschitz coefficients. As an application of such estimates, we study the size…

We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover…

In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients, we are interested in a Carleman-type inequality for these solutions satisfying an additional growth condition in elliptic…

This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…

In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman…

We consider a first-order transport equation $\ppp_tu(x,t) + (H(x)\cdot\nabla u(x,t)) + p(x)u(x,t) = F(x,t)$ for $x \in \OOO \subset \R^d$, where $\OOO$ is a bounded domain and $0<t<T$. We prove a Carleman estimate for more generous…

We consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman…

The motivation of this paper is to study a second order elliptic operator which appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant $r$-mean curvature. We prove a generalized Bochner-type…

In this paper we study quantitative uniqueness estimates of solutions to general second order elliptic equations with magnetic and electric potentials. We derive lower bounds of decay rate at infinity for any nontrivial solution under some…

We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quantitative sampling and equidistribution theorems for…

In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal…

The main purpose of this work is to study an inverse coefficient problem for the telegrapher's equations on a tree-shaped network. To analyze the stability for this inverse problem, Carleman estimate is established first. Based upon this…