Elias Wegert, George Khimshiashvili, and Ilya Spitkovsky

Nonlinear Transmission Problems

An existence theorem for solutions of non-linear transmission problems is proved using certain special estimates of inverses of Toeplitz operators. A framework for construction of analytic discs attached to singular targets is described, and a mechanism of creating such discs is presented.

Mathematics Subject Classification: 30E25, 32F35, 32S05.

Key words and phrases: Transmission problems, Toeplitz operators, analytic discs.