《变分学中的多重积分》(作者莫里)包含了大量科研人员学习多重积分变分问题和双曲偏微分方程问题的材料。书中不仅是作者科研成果的总结，更是同时代该领域或者相关领域的专业人士的巨大贡献。本书无疑会成为该领域科研人员的标准差参考书。本书的主要读者是对数学分析有一定基础的人员，分析专业的学生将会受益匪浅。

Chapter 1 Introduction

1.1. Introductory remarks

1.2. The plan of the book: notation

1.3. Very brief historical remarks

1.4. The euler equations

1.5. Other classical necessary conditions

1.6. Classical sufficient conditions

1.7. The direct methods

1.8. Lower semicontinuity

1.9. Existence

1.10. The differentiability theory. introduction

1.11. Differentiability; reduction to linear equations

Chapter 2 Semi-classical results

2.1. Introduction

2.2. Elementary properties of harmonic functions

2.3. Weyl's lemma

2.4. Poisson's integral formula; elementary functions; GREEN'S functions

2.5. Potentials

2.6. Generalized potential theory; singular integrals

2.7. The calderon-zygmund inequalities

2.8. The maximum principle for a linear elliptic equation of the second order

Chapter 3 The spaces Hmp and Hmp0

3.1. Definitions and first theorems

3.2. General boundary values; the spaces hmp0 (g); weak convergence

3.3. The dirichlet problem

3.4. Boundary values

3.5. Examples; continuity; some sobolev lemmas

3.5. Miscellaneous additional results

3.7. Potentials and quasi-potentials; generalizations

Chapter 4 Existence theorems

4.1. The lower-semicontinuity theorems of SERRIN

4.2. Variational problems with f = f(p); the equations (i. t 0. t 3) with n = i, bi=0, aα = aα(p)

4.3. The borderline cases k = v

4.4. The general quasi-regular integral

Chapter 5 Differentiability of weak solutions

5.1. Introduction

5.2. General theory; V >2

5.3. Extensions Of The DE giorgi-nash-moser results; V >2

5.4. The case V=2

5.5. Lp and SCHAUDER estimates

5.6. The Equation a.▽2u+b.▽u+cu-λu=f

5.7. Analyticity of the solutions of analytic linear equations

5.8. Analyticity of the solutions of analytic, non-linear, elliptic equations

5.9. Properties of the extremals; regular cases

5.10. The extremals in the case 1 <k < 2

5.11. The THEORY OF LADYZENSAYA AND URAL'TSEVA

5.12. A class of non-linear equations

Chapter 6 Regularity theorems for the solutions of general elliptic systems and boundary value problems

6.1. Introduction

6.2. Interior estimates for general elliptic systems

6.3. Estimates near the boundary; coerciveness

6.4. Weak solutions

6.5. The existence theory for The DIRICHLET problem for strongly elliptic systems

6.6. The analyticity of the solutions of analytic systems of linear elliptic equations

6.7. The analyticity of the solutions of analytic nonlinear elliptic systems

6.8. The differentiability of the solutions of non-linear elliptic systems; weak solutions; a perturbation theorem

Chapter 7 A variational method in the theory of harmonic integrals

7.1. Introduction

7.2. Fundamentals; The GAFFNEY-GARDING inequality

7.3. The variational method

7.4. The decomposition theorem. final results for compact manifolds with-out boundary

7.5. Manifolds with boundary

7.6. Differentiability at the boundary

7.7. Potentials, the decomposition theorem

7.8. Boundary value problems

Chapter 8 Theδ-NEUMANN problem on strongly pseudo-convex manifolds

8.1. Introduction

8.2. Results. Examples. The analytic embedding theorem

8.3. Some important formulas

8.4. The HXLBERT space results

8.5. The local analysis

8.6. The smoothness results

Chapter 9 Introduction to parametric integrals; two dimensional problem,

9.1. Introduction. parametric integrals

9.2. A lower semi-continuity theorem

9.3. Two dimensional problems; introduction; the conformal mapping of surfaces

9.4. The problem of plateau

9.5. The general two-dimensional parametric problem

Chapter 10 The higher dimensional PLATEAU problems

10.1. Introduction

10.2. v surfaces, their boundaries, and their HAUSDORFF measures

10.3. The topological results of ADAMS

10.4. The minimizing sequence; the minimizing set

10.5. The local topological disc property

10.6. The REIFENBERG cone inequality

10.7. The local differentiability

10.8. Additional results of federer concerning LEBESGUE v-area

Bibliography

Index