Plateau's Problem: the Douglas-Radó Theorem

Plateau’s problem concerns the existence of a surface of least area bounded by a given closed curve. The main focus of this thesis is the Douglas-Radó theorem, which, in the parametric formulation of the problem, guarantees the existence of a minimal surface bounded by a given Jordan curve in R^n. After introducing the variational approach, we use harmonic functions and the Courant-Lebesgue lemma to present a complete proof of the result.