Varational Formulation of Elliptic Partial Differential Equation
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Date
2024-07
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Addis Ababa University
Abstract
The focus of this thesis is to examine weak or variational formulations of various elliptic boundary value problems and determine whether or not they are well-posed. The weak version of the homogeneous Dirichlet boundary value problem for the Poisson equation is first derived. A weak formulation can be thought of as an operator equation in its abstract form. Additionally, we offer some broad conclusions on the existence and uniqueness of linear operator equations.
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Keywords
Varational Formulation, Elliptic Partial, Differential Equation