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HILBERT BOUNDARY VALUE PROBLEM OF NON-NORMAL TYPE FOR ANALYTIC FUNCTIONS

Jinyuan Du

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Abstract

In this paper, Hilbert boundary value problem of non-normal type for analytic function is considered. The problem is transformed to normal Riemann boundary value problem by the method of symmetric extension. The solution to the problem and the condition of solvability are obtained. Meanwhile, by using the Peano derivative, a necessary condition for the solvability of the problem is given.

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What this paper is about

In this paper, Hilbert boundary value problem of non-normal type for analytic function is considered. The problem is transformed to normal Riemann boundary value problem by the method of symmetric extension. The solution to the problem and the condition of solvability are obtained. Meanwhile, by using the Peano derivative, a necessary condition for the solvability of the problem is given.

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Available abstract

In this paper, Hilbert boundary value problem of non-normal type for analytic function is considered. The problem is transformed to normal Riemann boundary value problem by the method of symmetric extension. The solution to the problem and the condition of solvability are obtained. Meanwhile, by using the Peano derivative, a necessary condition for the solvability of the problem is given.

Key concepts: Mathematics, Boundary value problem, Peano axioms, Analytic function, Mathematical analysis, Riemann–Hilbert problem, Free boundary problem, Type (biology)

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