In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second funda...In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.展开更多
The purpose of this paper is to complement the results by Lanzani and Stein(2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani and Stein(201...The purpose of this paper is to complement the results by Lanzani and Stein(2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani and Stein(2017), where L^p-boundedness is shown to fail when either the "near" C^2 boundary regularity, or the strong C-linear convexity assumption is dropped.展开更多
In this paper, we study the boundary-value problem for mixed type equation with singular coefficient. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the ...In this paper, we study the boundary-value problem for mixed type equation with singular coefficient. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the existence is based on the theory of singular integral equations, Wiener-Hopf equations and Fredholm integral equations.展开更多
The purpose of this paper is to complement the results by Lanzani and Stein （2017） by showing thedense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani andStein （...The purpose of this paper is to complement the results by Lanzani and Stein （2017） by showing thedense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani andStein （2017）, where LP-boundedness is shown to fail when either the ＂near＂ C2 boundary regularity, or the strongC-linear convexity assumption is dropped.展开更多
Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main resu...Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.展开更多
基金supported by NNSF of China(11171260)RFDP of Higher Education of China(20100141110054)+3 种基金NSF of Fujian ProvinceChina(2008J0187)STF of Education Department of Fujian ProvinceChina(JA11341)
文摘In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.
基金supported by the National Science Foundation of USA (Grant Nos. DMS1503612 (Lanzani) and DMS-1265524 (Stein))
文摘The purpose of this paper is to complement the results by Lanzani and Stein(2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani and Stein(2017), where L^p-boundedness is shown to fail when either the "near" C^2 boundary regularity, or the strong C-linear convexity assumption is dropped.
文摘In this paper, we study the boundary-value problem for mixed type equation with singular coefficient. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the existence is based on the theory of singular integral equations, Wiener-Hopf equations and Fredholm integral equations.
基金supported by the National Science Foundation of USA (Grant Nos. DMS1503612 (Lanzani) and DMS-1265524 (Stein))
文摘The purpose of this paper is to complement the results by Lanzani and Stein （2017） by showing thedense definability of the Cauchy-Leray transform for the domains that give the counter-examples of Lanzani andStein （2017）, where LP-boundedness is shown to fail when either the ＂near＂ C2 boundary regularity, or the strongC-linear convexity assumption is dropped.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10626054,10701077)the Knowledge Innovation Project of Chinese Academy of Sciences(Grant No.KJCX3-SYW-S03)the National Key Basic Research Project of China(Grant No.2004CB31800,2006CB805905)
文摘Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.
