Existence of solution in weighted Sobolev space W_n,p(D; d^μ(z; ∂D)) to Riemann–Hilbert problem with piece-wise continuous boundary data for non-homogeneous polyanalytic equation of order n

Abstract

The given non-homogeneous polyanalytic differential equation is transformed into an equivalent system of integro–differential equations before its general solution in the weighted Sobolev space W _n,p (D; d ^μ(z, ∂D)) is sought using functional analytic tools. The boundary value problem is then solved by first transforming it to two analogous problems for polyanalytic functions. The latter was already solved by the author in a separate study.

Keywords:

• Polyanalytic function
• Weighted Sobolev space
• Cauchy–Pompeiu integral operators of higher order
• Riemann–Hilbert problem
• Classification Categories: 30G20
• 35G15
• 35J40

Acknowledgements

This work was carried out during the author's visit to the Abdus Salam International Centre for Theoretical Physics in Trieste, Italy, in his capacity as Senior Associate. The author expresses herewith his sincere thanks to the Centre and SIDA which supports the Associate programme.

Notes

On the occasion of the 65th birthday of my teacher, Prof. Heinrich Begehr.

Email: [email protected]; [email protected]

Email: [email protected]; [email protected]

Additional information

Notes on contributors

Ali Seif Mshimba *

On the occasion of the 65th birthday of my teacher, Prof. Heinrich Begehr. Email: [email protected]; [email protected]