内容

目次

1. Introduction PART I: REPRESENTATION FORMULAS FOR SOLUTIONS 2. Four Important Linear PDE 3. Nonlinear First-Order PDE 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