The Stability of the Riemann Boundary Value Problem for Vector Valued M-Analytic Functions
In this paper, certain boundary value problems are solved in a Banach space which is defined by vector-valued regular solutions of the systemm f x + M f y = 0 of elliptic partial differential equations, where M is a constant m × m matrix without real eigenvalues and f is an m × q matrix. The properties of the integral of Cauchy type for vector-valued M-analytic functions are discussed. Next, the representation of the solutions of the Riemann boundary value problem and its pertubed problem for vector-valued M-analytic functions are presented.
KeywordsSingular Integral Equation Finite Order Polynomial Matrix Elliptic Partial Differential Equation Cauchy Type
Unable to display preview. Download preview PDF.
- Hill, G.N. : Elliptic systems in the plane with first order terms and constant coefficients. Comm. Part. Diff. Eq. 3 (1978), 947–977.Google Scholar
- Hille E., Phillips, R.S.: Functional Analysis and Semi-Groups. Amer. Math. Soc. Colloq. Publ., Amer. Math. Soc, Providence, RI, 1957.Google Scholar
- Hu, C.G. : Vector-valued boundary value problems of a class, Proceedings on International Conference on Integral Equations and Boundary Value Problems, ed. G.-C. Wen, Z. Zhao. World Scientific, Singapore, New Jersey, London, Hong Kong, 1991, 57–64.Google Scholar
- Hu, C.G. : Linear systems of a class in locally convex spaces, Complex analysis and its applications, ed. C.C. Yang et. al. Pitman Research Notes in Mathematics Series 305, Longman Scientific & Technical, Harlow, 1994, 90–199.Google Scholar