A Mixed Boundary Value Problem for Polyanalytic Function of Order n in the Sobolev Space Wn,p (D) |
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Abstract: | We discuss the construction of a polyanalytic function Φ of order n on a simple bounded domain D. The function satisfies n prescribed generalized Riemann-Hilbert boundary conditions on the boundary ?D and n generalized jump conditions on a simple closed smooth contour γ contained in D. The boundary conditions are transformed into n classical Riemann-Hilbert problems and the n jump conditions into n Riemann problems of conjugation for some 2n holomorphic functions. These transformed problems are solved using the standard methods from the literature. |
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Keywords: | Polyanalytic Function Riemann-Hilbert Problem Riemann Problem Of Linear Conjugation |
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