Carro Rossell, María JesúsNaibo, VirginiaSoria Carro, María2026-01-142026-01-14202510.1016/j.jde.2025.113216https://hdl.handle.net/20.500.14352/130247We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower half planes. Our techniques are based on the use of conformal maps and Rellich identities for the Hilbert transform, and are motivated by previous works concerning the Dirichlet, Neumann and Zaremba problems.engjournal articlehttps://doi.org/10.1016/j.jde.2025.113216open accessTransmission problemsGraph simply connected domainsConformal mapsMuckenhoupt weightsMatemáticas (Matemáticas)Análisis matemático12 Matemáticas