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【期刊论文】Fourier Method for an Over-Determined Elliptic System with Several Complex Variables
戴道清, Dao Qing DAI
,-0001,():
-1年11月30日
Two boundary value problems are investigated for an over-determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independent solutions and finitely many solvability conditions are derived. Moreover, the boundary value problem for any number of complex variables is treated in a unified way and the essential dierence between the case of one complex variable and that of several complex variables is revealed.
Several complex variables,, Analytic functions,, Riemann problem,, Riemann-Hilbert problem,, Over-determined elliptic system
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【期刊论文】On continuous solutions of a generalized Cauchy-Riemann system with more than one singularity
戴道清, Heinrich Begehr a, * and Dao-Qing Dai b,
J. Differential Equations 196(2004)67-90,-0001,():
-1年11月30日
We study the solvability of the Riemann-Hilbert problem for a generalized Cauchy-Riemann system with several singularities and reveal several new phenomenon. For the number of continuous solutions we shall show that it depends not only on the index but also on the location and type of the singularities; moreover, it does not depend continuously on the coefficients of the equation.
Boundary value problem, Singular coefficient, Generalized analytic function, A priori estimate, Continuous solution
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