Solution of initial value problems for pseudoholomorphic functions in conical domains

Celebi, AO
Yuksel, U
It had previously been proved [U. Yüksel and A. O. Çelebi, Complex Variables Theory Appl. 29, No. 4, 305–311 (1996; Zbl 0852.30027)] that the initial value problem (1) ∂w/∂t=Lw, w(0,z)=w 0 (z), where the operator L is defined by (2) Lw:=E 0 (t,z)∂ ∂z ¯d E w dz+F 0 (t,z)∂ ∂z ¯ d E w dz ¯+C 0 (t,z)d E w dz+G 0 (t,z)d E w dz ¯+A 0 (t,z)w+B 0 (t,z)w ¯+D 0 (t,z) in the space P D (E) of pseudoholomorphic functions in the sense of Bers, turns out to be solvable by the abstract Cauchy-Kovalevskaya theorem. The present paper is aimed at solving the initial value problems (1) by the contraction-mapping principle in conical domains.


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Citation Formats
A. Celebi and U. Yuksel, “Solution of initial value problems for pseudoholomorphic functions in conical domains,” 1997, vol. 1, p. 65, Accessed: 00, 2020. [Online]. Available: