文档介绍：Lecture Notes in Mathematics
An informal series of special lectures, seminars and reports on mathematical topics
Edited by A. Dold, Heidelberg and B. Eckmann, ZUrich
8 [_!
Gaetano Fichera
University of Rome
Linear elliptic
differential systems and
eigenvalue problems
1965 The Johns Hopkins University, Baltimore Md, March- May 1965
Springer-Verlag. Berlin Heidelberg New York
All rights, especially that oftranalafion into foreign languages, reserved. It is also forbidden to reproduce this book, either
whole or in part, by photomechanical (photostat, microfilm and/or microcard)or by other procedure without
written permission from Springer Verlag. @ by Springer-Verlag Berlin Heidelberg 1965.
Library of Congress Catalog Card Number 65--27796. Printed in Germany. Title No. 7328
These Notes contain the lectures I had the pleasure
of delivering as Visiting Professor at the Department of ~echanics
of The Johns Hopkins University on the invitation of Professor
Clifford Truesdell.
They are intended to be an introduction to the modern
approach to higher order elliptic boundary value problems and related
eigenvalue problems.
I am deeply grateful to Dr. Warren Edelstein for his
kind collaboration in checking both the English and the Mathematics
of these Notes.
G. Fichera
Baltimores Md. -Liay 1965.
CONTENTS
Lecture 1. "Well posed" boundar 7 value problems ....................... 1
Lectnre 2 Existenc e principle ~ ..................................... ~ 11
O
Lecture 3~ The function spaces Hm and Hm ...o ..................... ... 17
Lecture 4~ The trace operator. Sobolev and Ehrling lethal. ............. 24
Lecture 6. Elliptic linear systems~ Interior regularity ~ ............... 30
Lecture 6.
Existence of local solutions fori elliptic systems ........... 39
Lecture 7 o Semiveak solutions of BVP for elliptic systems ........... ... 44
Lecture 8. Regularity at the boundary: preliminar 7 ~s