文档介绍：Copyright e 1995 by Princeton University Press
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Library ofCongress Cataloging-in-Publication Data
Folland, G. B.
Introduction to partial differential equations I Gerald B. Folland.•
2nd ed.
p. em.
Includes bibliographical references and indexes.
ISBN 0-691-04361-2 (el: alk. paper)
1. Differential equations, Partial. I. Tide.
1995 95-32308
515'')53-dc20
The publisher would like to acknowledge the author of this volume for
providing the camera-ready copy from which this book. was printed
Princeton University Press books are printed on acid-free paper and
meet the guidelines for permanence and durability mittee
on Production Guidelines for Book Longevity ofthe Council on
Library Resources
Printed in the United States ofAmerica
by Princeton Academic Press
10 9 8 7 6 S 4 3 2 I
I
t
CONTENTS
PREFACE ix
Chapter 0
PRELIMINARIES 1
A. Notations and Definitions 1
B. Results from Advanced Calculus 4
C. Convolutions 9
D. The Fourier Transform 14
E. Distributions 17
F. Compact Operators 22
Chapter 1
LOCAL EXISTENCE THEORY 30
A. Basic Concepts 30
B. Real First Order Equations 34
C. The General Cauchy Problem 42
D. The Cauchy-Kowalevski Theorem 46
E. Local Solvability: the Lewy Example 56
F. Constant-Coefficient Operators: Fundamental Solutions 59
Chapter 2
THE LAPLACE OPERATOR 66
A. Symmetry Properties of the Laplacian 67
B. Basic Properties of Harmonic Functions 68
C. The Fundamental Solution 74
D. The Dirichlet and Neumann Problems 83
E. The Green's Function 85
F. Dirichlet's Principle 88
G. The Dirichlet Problem in a Half-Space 91
H. The Dirichlet Problem in a Ball 95
I. More about Harmonic Functions 110
vi Contents
Chapter 3
LAYER POTENTIALS 116
A. The Setup 116
B. Integral