Solution of initial value problems for pseudoholomorphic functions in conical domains

Abstract

It has been proved previously [8] that the initial-value problem

where the operator L is defined by

in the space pD(E) of pseudoholomorphic functions in the sense P_D(E) of Bers turns out to be solvable by the abstract Cauchy-Kowalewski theorem.

The present paper is aimed at solving the initial-value problem (1) by the contraction-mapping principle in conical domains.

Keywords:

• Cauchy-Kowalewski
• Bers
• pseudoholomorphic

Classification Categories::

• 30G20
• 35A10
• 35F10