The problem of uniqueness of entire functions is dealt with. It is shown that there exists a finite set S such that any two nonconstant entire functions f and g satisfying Ef(S) = Eg(S) must be identical, which answer...The problem of uniqueness of entire functions is dealt with. It is shown that there exists a finite set S such that any two nonconstant entire functions f and g satisfying Ef(S) = Eg(S) must be identical, which answers an open question posed by Gross.展开更多
The unique continuation on quadratic curves for harmonic functions is dis-cussed in this paper.By using complex extension method,the conditional stability of unique continuation along quadratic curves for harmonic fun...The unique continuation on quadratic curves for harmonic functions is dis-cussed in this paper.By using complex extension method,the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated.The nu-merical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.展开更多
In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are ...In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are proved.展开更多
In this paper, properties of the spherical functions and Hardy-Sobolev inequalities of generalized Baouendi-Grushin vector fields are established, and then some unique continuation results for generalized Baouendi Gru...In this paper, properties of the spherical functions and Hardy-Sobolev inequalities of generalized Baouendi-Grushin vector fields are established, and then some unique continuation results for generalized Baouendi Grushin operators with singular weights are given.展开更多
The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carlem...The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.展开更多
In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open boun...In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open bounded domain,we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain.Using the corresponding Riemann function,we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives.Further,we construct several examples showing the possibility of further reducing the additional information of the other component.This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The problem of uniqueness of entire functions is dealt with. It is shown that there exists a finite set S such that any two nonconstant entire functions f and g satisfying Ef(S) = Eg(S) must be identical, which answers an open question posed by Gross.
基金This work was supported by the National Natural Science Foundation of China(No.11971121).
文摘The unique continuation on quadratic curves for harmonic functions is dis-cussed in this paper.By using complex extension method,the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated.The nu-merical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.
基金supported by the National Natural Science Foundation of China(10871157)Research Fund for the Doctoral Program of Higher Education of China(200806990032)Keji Chuangxin Jijin of Northwestern Polytechnical University(2007KJ01012)
文摘In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are proved.
基金Supported by National Natural Science Foundation of China （Grant No. 10871157）, Research Fund for the Doctoral Program o[ Higher Education of China （Grant No. 200806990032）
文摘In this paper, properties of the spherical functions and Hardy-Sobolev inequalities of generalized Baouendi-Grushin vector fields are established, and then some unique continuation results for generalized Baouendi Grushin operators with singular weights are given.
文摘The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.
基金supported by the A3 Foresight Program“Modeling and Computation of Applied Inverse Problems”Japan Society for the Promotion of Science(JSPS)+5 种基金National Natural Science Foundation of China(NSFC)supported by NSFC(No.11971121)partially supported by JSPS KAKENHI Grant Number JP15H05740supported by NSFC(No.11771270)partly supported by NSFC(No.91730303)RUDN University Program5-100。
文摘In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open bounded domain,we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain.Using the corresponding Riemann function,we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives.Further,we construct several examples showing the possibility of further reducing the additional information of the other component.This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution.
