Dirichlet problem for Poisson equations in Jordan domains - Gutlyanskii, V.; Ryazanov, V.; Yakubov, E. (Праці Інституту прикладної математики і механіки НАН України, 2018)
We study the Dirichlet problem for the Poisson equations △u(z) = g(z) with g ∈ Lp, p > 1, and continuous boundary data φ : ∂D → ℝ in arbitrary Jordan domains D in ℂ and prove the existence of continuous solutions u of the problem.