Related papers: Quantitative uniqueness of solutions to second ord…
We investigate the quantitative unique continuation properties of solutions to second order elliptic equations with singular lower order terms. The main theorem presents a quantification of the strong unique continuation property for…
We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique…
In this article, we study the vanishing order of solutions to second order elliptic equations with singular lower order terms in the plane. In particular, we derive lower bounds for solutions on arbitrarily small balls in terms of the…
In this paper we derive quantitative uniqueness estimates at infinity for solutions to an elliptic equation with unbounded drift in the plane. More precisely, let $u$ be a real solution to $\Delta u+W\cdot\nabla u=0$ in ${\mathbf R}^2$,…
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…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
We investigate the quantitative uniqueness of solutions to parabolic equations with lower order terms on compact smooth manifolds. Quantitative uniqueness is a quantitative form of strong unique continuation property. We characterize…
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…
In this paper, we focus on the quantitative unique continuation property of solutions to \begin{equation*} \Delta^2u=Vu, \end{equation*} where $V\in W^{1,\infty}$. We show that the maximal vanishing order of the solutions is not large than…
In this work, we investigate the quantitative estimates of the unique continuation property for solutions of an elliptic equation $\Delta u = V u + W_1 \cdot \nabla u + \hbox{div} (W_2 u)$ in an open, connected subset of $\mathbb{R}^d$,…
We address the quantitative uniqueness properties of the solutions of the parabolic equation $ \partial_t u - \Delta u = w_j (x,t) \partial_j u + v(x,t) u $ where $v$ and $w$ are bounded. We prove that for solutions $u$, the order of…
In this article, we study a quantitative form of the Landis conjecture on exponential decay for real-valued solutions to second order elliptic equations with variable coefficients in the plane. In particular, we prove the following…
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…
Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property. For the first time, we investigate the…
In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong…
We study quantitative unique continuation for second order elliptic equations with lower-order terms of H\"older regularity via a weighted frequency function method. We establish quantitative three-ball inequalities and corresponding…
In this article, we study the order of vanishing and a quantitative form of Landis' conjecture in the plane for solutions to second-order elliptic equations with variable coefficients and singular lower order terms. Precisely, we let $A$ be…
In this paper we study the local behavior of a solution to the $l$th power of Laplacian with singular coefficients in lower order terms. We obtain a bound on the vanishing order of the nontrivial solution. Our proofs use Carleman estimates…
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…
In this article, we investigate the quantitative unique continuation properties of complex-valued solutions to drift equations in the plane. We consider equations of the form $\Delta u + W \cdot \nabla u = 0$ in $\mathbb{R}^2$, where $W =…