The Cauchy problem in Sobolev spaces for Dirac operators

被引：0

作者：

I. V. Shestakov

机构：

[1] Institute of Mathematics,

来源：

Russian Mathematics | 2009年 / 53卷 / 7期

关键词：

Cauchy problem; Dirac operators; Carleman formula;

D O I：

10.3103/S1066369X09070056

中图分类号：

学科分类号：

摘要：

In this paper we consider the Cauchy problem as a typical example of ill-posed boundary-value problems. We obtain the necessary and (separately) sufficient conditions for the solvability of the Cauchy problem for a Dirac operator A in Sobolev spaces in a bounded domain D ⊂ ℝn with a piecewise smooth boundary. Namely, we reduce the Cauchy problem for the Dirac operator to the problem of harmonic extension from a smaller domain to a larger one.

引用

页码：43 / 54

页数：11

共 6 条

[1]

Solomyak M. Z.(1963)On Linear Elliptic Systems of the First Order Sov. Phys. Dokl 150 48-51

[2]

Shlapunov A. A.(1995)Bases with Double Orthogonality in the Cauchy Problem for Systems with Injective Symbols Proc. London Math. Soc. 71 1-52

[3]

Tarkhanov N. N.(1991)On the Possibility of Holomorphic Extension into a Domain of Functions Defined on a Connected Piece of Its Boundary Matem. Sborn. 182 490-507

[4]

Aizenberg L. A.(1992)On the Cauchy problem for Laplace’s Operator Sib. Matem. Zhurn. 33 205-215

[5]

Kytmanov A. M.(undefined)undefined undefined undefined undefined-undefined

[6]

Shlapunov A. A.(undefined)undefined undefined undefined undefined-undefined

← 1 →