Related papers: Quantitative uniqueness of elliptic equations
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…
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 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…
We establish the strong unique continuation property of fractional orders of linear elliptic equations with Lipschitz coefficients by establishing monotonicity of some Almgren-type frequency functional via an extension procedure.
In this article, we study the quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms. We quantify the strong unique continuation property by estimating the maximal vanishing order of…
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…
Based on a variant of the frequency function approach of Almgren, we establish an optimal upper bound on the vanishing order of solutions to variable coefficient Schr\"odinger equations at a portion of the boundary of a $C^{1,Dini}$ domain.…
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 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…
Based on a variant of the frequency function approach of Almgren, we establish an optimal bound on the vanishing order of solutions to stationary Schr\"odinger equations associated to a class of subelliptic equations with variable…
We study the quantitative unique continuation property of some higher order elliptic operators. In the case of $P=(-\Delta)^m$, where $m$ is a positive integer, we derive lower bounds of decay at infinity for any nontrivial solutions under…
Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good understanding of the vanishing order and size of singular and zero…
We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.
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 ${\mathbf R}^2$,…
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schr\"odinger operators and control theory. We review recent results and announce new ones regarding…
This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals depending on the gradient, as well as more general double…
We give a sharp upper bound on the vanishing order of solutions to Schr\"odinger equation, in the case that the potential is of class $\mathcal{C}^1$ on a smooth compact manifold.
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…
Based on a variant of the frequency function approach of Almgren([Al]), we establish an optimal upper bound on the vanishing order of solutions to stationary Schr\"odinger equations associated to sub-Laplacian on Carnot groups of arbitrary…
In this survey we discuss the frequency function method so as to study the problem of unique continuation for elliptic partial differential equations. The methods used in the note were mainly introduced by Garofalo and Lin.