Existence of solution in weighted Sobolev space W n,p (D; dμ(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.