Unique continuation along an analytic curve for the elliptic partial differential equations
نویسنده
چکیده
We consider an elliptic partial di erential operator P (x; @) with analytic coe cients and discuss the unique continuation along an analytic curve. That is, let P (x; @)u = 0 in a simply connected domain R, be an analytic curve and let fxgj2N have an accumulation point. Our main result asserts that if u(x) = 0, j 2 N , then u(x) = 0 for any x 2 . Furthermore we apply such uniqueness to an isotropic Lam e system with constant Lam e coe cients and the Kirchho plate equation with analytic coe cients.
منابع مشابه
Unique Continuation and Complexity of Solutions to Parabolic Partial Differential Equations with Gevrey Coefficients
In this paper, we provide a quantitative estimate of unique continuation (doubling property) for higher-order parabolic partial differential equations with non-analytic Gevrey coefficients. Also, a new upper bound is given on the number of zeros for the solutions with a polynomial dependence on the coefficients.
متن کاملA numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method
In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.
متن کاملHybrid Inverse Problems and Redundant Systems of Partial Differential Equations
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step that is not considered in this paper, provides internal information combining unknown parameters and solutions of differential equations. In several settings, ...
متن کاملPartial Differential Equations applied to Medical Image Segmentation
This paper presents an application of partial differential equations(PDEs) for the segmentation of abdominal and thoracic aortic in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been exte...
متن کاملLinear Elliptic Equations of Second Order
3 4 CONTENTS Preface These lecture notes are intented as an introduction to linear second order elliptic partial differential equations. It can be considered as a continuation of a chapter on elliptic equations of the lecture notes [17] on partial differential equations. In [17] we focused our attention mainly on explicit solutions for standard problems for elliptic, parabolic and hyperbolic eq...
متن کامل