Wyman, Jeffries2017-12-212017-12-2119601960b14708292https://hdl.handle.net/2144/26084Thesis (M.A.)--Boston UniversityThe problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as the Dirichlet Problem. In this paper I consider the special eliptic equation of ∇2 J=0 which is Laplace's equation, and I limit myself to the case of two dimensions. Subject to these limitations I discuss five proofs for the existence of a solution to Laplace's equation for arbitrary regions where the boundary values are given. [TRUNCATED]en-USBased on investigation of the BU Libraries' staff, this work is free of known copyright restrictions.Dirichlet problemPartial differential equationThesis/Dissertation