SES # | TOPICS | KEY DATES |
---|---|---|

1–2 | Review of Harmonic Functions and the Perspective We Take on Elliptic PDE | |

3 | Finding Other Second Derivatives from the Laplacian | |

4 | Korn’s Inequality I | |

5 | Korn’s Inequality II | Problem Set 1 due |

6 | Schauder’s Inequality | |

7 | Using Functional Analysis to Solve Elliptic PDE | |

8 | Sobolev Inequality I | |

9 | Sobolev Inequality II | |

10–12 | De Giorgi-Nash-Moser Inequality | Problem Set 2 due |

13 | Nonlinear Elliptic PDE I | |

14 | Nonlinear Elliptic PDE II | |

15 | Barriers | |

16–17 | Minimal Graphs | Problem Set 3 due |

18–19 | Leray-Schauder Approach to Nonlinear PDE | |

20 | Gauss Circle Problem I | |

21 | Gauss Circle Problem II | |

22–24 | Fourier Analysis in PDE and Interpolation | |

25 | Applications of Interpolation | |

26 | Calderon-Zygmund Inequality I | |

27 | Calderon-Zygmund Inequality II | Problem Set 4 due |

28 | Littlewood-Paley Theory | |

29 | Strichartz Inequality I | |

30 | Strichartz Inequality II | |

31–34 | The Nonlinear Schrödinger Equation | Problem Sets 5 and 6 due |

## Calendar

## Course Info

##### Learning Resource Types

*assignment*Problem Sets

*notes*Lecture Notes