偏微分方程(第2版)(英文版)(精)/美国数学会经典影印系列

这是当今《偏微分方程》（PDE）权威教材的第 二版。它给出了PDE理论学习中现代技术的总览，特 别注重非线性方程。本书内容广泛、阐述清晰，已经 是PDE方面经典的研究生教材。在本版中，作者劳伦 斯·埃文斯做了大量改动，包括：新增非线性波动方 程的一章；超过80个新习题；许多新的小节；大大扩 充了参考文献。

Preface to second edition Preface to first edition 1. Introduction 1.1. Partial differential equations 1.2. Examples 1.2.1. Single partial differential equations 1.2.2. Systems of partial differential equations 1.3. Strategies for studying PDE 1.3.1. Well-posed problems, classical solutions 1.3.2. Weak solutions and regularity 1.3.3. Typical difficulties 1.4. Overview 1.5. Problems 1.6. References PART I: REPRESENTATION FORMULAS FOR SOLUTIONS 2. Four Important Linear PDE 2.1. Transport equation 2.1.1. Initial-value problem 2.1.2. Nonhomogeneous problem 2.2. Laplace's equation 2.2.1. Fundamental solution 2.2.2. Mean-value formulas 2.2.3. Properties of harmonic functions 2.2.4. Green's function 2.2.5. Energy methods 2.3. Heat equation 2.3.1. Fundamental solution 2.3.2. Mean-value formula 2.3.3. Properties of solutions 2.3.4. Energy methods 2.4. Wave equation 2.4.1. Solution by spherical means 2.4.2. Nonhomogeneous problem 2.4.3. Energy methods 2.5. Problems 2.6. References 3. Nonlinear First-Order PDE 3.1. Complete integrals, envelopes 3.1.1. Complete integrals 3.1.2. New solutions from envelopes 3.2. Characteristics 3.2.1. Derivation of characteristic ODE 3.2.2. Examples 3.2.3. Boundary conditions 3.2.4. Local solution 3.2.5. Applications 3.3. Introduction to Hamilton-Jacobi equations 3.3.1. Calculus of variations, Hamilton's ODE 3.3.2. Legendre transform, Hopf-Lax formula 3.3.3. Weak solutions, uniqueness 3.4. Introduction to conservation laws 3.4.1. Shocks, entropy condition 3.4.2. Lax-Oleinik formula 3.4.3. Weak solutions, uniqueness …… 4. Other Ways to Represent Solutions PART II: THEORY FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS 5. Sobolev Spaces 6. Second-Order Elliptic Equations 7. Linear Evolution Equations PART III: THEORY FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS 8. The Calculus of Variations 9. Nonvariational Techniques 10. Hamilton-Jacobi Equations 11. Systems of Conservation Laws 12. Nonlinear Wave Equations APPENDICES Appendix A: Notation Appendix B: Inequalities Appendix C: Calculus Appendix D: Functional Analysis Appendix E: Measure Theory Bibliography Index