AV Bitsadze's observation on bianalytic functions and the Schwarz problem


AKSOY Ü., Begehr H., ÇELEBİ A. O.

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, cilt.64, ss.1257-1274, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 64 Konu: 8
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1080/17476933.2018.1504039
  • Dergi Adı: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
  • Sayfa Sayıları: ss.1257-1274

Özet

According to an observation of A.V. Bitsadze from 1948 the Dirichlet problem for bianalytic functions is ill-posed. A natural boundary condition for the polyanalytic operator, however, is the Schwarz condition. An integral representation for the solutions in the unit disc to the inhomogeneous polyanalytic equation satisfying Schwarz boundary conditions is known. This representation is extended here to any simply connected plane domain having a harmonic Green function. Some other boundary value problems are investigated with some Dirichlet and Neumann conditions illuminating that just the Schwarz problem is a natural boundary condition for the Bitsadze operator.