Penning, F.D.2024-11-272024-11-2722/01/281981http://hdl.handle.net/2263/99465Dissertation (MSc (Mathematics))--University of Pretoria, 1981.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.en© 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.RegulariteitstellingsElliptieseRandwaardeproblemeUCTDDissertation