Regulariteitstellings vir elliptiese randwaardeprobleme

Abstract

In this thesis the regularity (differentiability) of weak solutions of a certain class of elliptic boundary value problems will be shown. For the proof of regularity theorems, one will resort mainly to the techniques of functional analysis. Regularity theorems will be proved progressively: firstly, regularity in the tangential direction on the boundary will be shown; then regularity of a certain class of second order elliptic boundary value problems will be demonstrated and lastly regularity in the normal direction on the boundary will be accounted for. Theorems will also be illustrated for second as well as higher order Dirichlet and Neumann boundary value problems. One should also mention that specific abstract Sobolev spaces play an important role in the proofs of most theorems.