Multiple Integrals in the Calculus of Variations (eBook)

Charles Bradfield Morrey Jr. (1907 - 1984) received a PhD degree in mathematics from Harvard University, Cambridge, MA, in 1931, and was awarded a National Research Council Fellowship afterwards that brought him to Princeton University, Princeton, NJ, from 1931 to 1932, and to the Rice Institute, Houston, TX, from 1932 to 1933. In 1933 he took a position at the Department of Mathematics at the University of California, Berkeley, where he was actively involved in teaching and research until his retirement in 1973. Morrey was an outstanding mathematician, known also as a very effective and successful teacher. He solved Hilbert’s Nineteenth Problem, and also contributed considerably to the solution of questions raised in Problem No. 20. Following in the footsteps of Leonida Tonelli, Morrey became the founder of the modern Calculus of Variations, and the present treatise is the mature fruit of his achievements. This and his other books have had and continue to have a wide influence on the teaching of mathematics. Morrey’s scientific accomplishments and his administrative abilities were complemented by his gift for friendship, his charming sense of humour, and his continuing concern for people, for mathematics, and for music. [Sources: S. Hildebrandt, and "In memoriam" by J.L. Kelley, D.H. Lehmer, R.M. Robinson, University of California]

Preface 8
Table of Contents 10
1 Introduction 14
2 Semi-classical results 52
3 The spaces Hmp and Hmp0 75
4 Existence theorems 103
5 Differentiability of weak solutions 139
6 Regularity theorems for the solutions of general elliptic systems and boundary value problems 222
7 A variational method in the theory of harmonic integrals 299
8 The 5-Neumann problem on strongly pseudo-convex manifolds 329
9 Introduction to parametric Integrals two dimensional problems
10 The higher dimensional plateau problems 413
Bibliography 507
Index 517