Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f sati...Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated.展开更多
The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions...The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces.This technique makes it also possible to solve ill-posed initial value problems.展开更多
In this paper, we study mixed elastico-plasticity problems in which part of the boundary is known, while the other part of the boundary is unknown and is a free boundary. Under certain conditions, this problem can be ...In this paper, we study mixed elastico-plasticity problems in which part of the boundary is known, while the other part of the boundary is unknown and is a free boundary. Under certain conditions, this problem can be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundary value problem for complex equations. Using the theory of generalized analytic functions, the solvability of the problem is discussed.展开更多
基金supported by NNSF of China (11171260)RFDP of Higher Education of China (20100141110054)Scientific Research Fund of Leshan Normal University (Z1265)
文摘Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated.
文摘The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces.This technique makes it also possible to solve ill-posed initial value problems.
基金the National Natural Science Foundation of China(No.10471149,10671207)the Postdoctoral Science Foundation of China(No.2005037447)
文摘In this paper, we study mixed elastico-plasticity problems in which part of the boundary is known, while the other part of the boundary is unknown and is a free boundary. Under certain conditions, this problem can be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundary value problem for complex equations. Using the theory of generalized analytic functions, the solvability of the problem is discussed.
