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Found 2 essays matching the above criteria.

1. 1. The History of the Dirichlet Problem for Laplace’s Equation

   University essay from Linköpings universitet/Analys och didaktik; Linköpings universitet/Tekniska fakulteten

   Author : Måns Alskog; [2023]
   Keywords : Potential Theory; Dirichlet Problem; Laplace’s Equation; Complex Analysis; Potentialteori; Dirichletproblemet; Laplaces ekvation; komplex analys;

   Abstract : This thesis aims to provide an introduction to the field of potential theory at an undergraduate level, by studying an important mathematical problem in the field, namely the Dirichlet problem. By examining the historical development of different methods for solving the problem in increasingly general contexts, and the mathematical concepts which were established to support these methods, the aim is to provide an overview of various basic techniques in the field of potential theory, as well as a summary of the fundamental results concerning the Dirichlet problem in Euclidean space. READ MORE

3. 2. Solving an inverse problem for an elliptic equation using a Fourier-sine series.

   University essay from Linköpings universitet/Matematiska institutionen

   Author : Olivia Linder; [2019]
   Keywords : Regularization; ill-posed problem; Fourier-sine series; Regularisering; illaställt problem; Fouriersinusserie;

   Abstract : This work is about solving an inverse problem for an elliptic equation. An inverse problem is often ill-posed, which means that a small measurement error in data can yield a vigorously perturbed solution. Regularization is a way to make an ill-posed problem well-posed and thus solvable. READ MORE