# 401-3350-21L Classical Theory of Elliptic Partial Differential Equations

Semester | Spring Semester 2021 |

Lecturers | J. Serra |

Periodicity | non-recurring course |

Language of instruction | English |

Comment | Number of participants limited to 12. |

### Courses

Number | Title | Hours | Lecturers | ||||
---|---|---|---|---|---|---|---|

401-3350-21 S | Classical Theory of Elliptic Partial Differential Equations | 2 hrs |
| J. Serra |

### Catalogue data

Abstract | Following the book "Elliptic Partial Differential Equations" of Qing Han and Fanhua Lin, the seminar will cover ---from an introductory perspective--- some important classical tools and results in the standard theory of Elliptic PDE |

Learning objective | To present some of the most useful classical tools and results in nonlinear Elliptic PDE (weak and viscosity solutions and their maximum principles, moving plane method, Bernstein's technique, De Giorgi-Nash-Moser Harnack Inequality, etc.) |

Content | (flexible depending on the background of the students) -Review of harmonic functions -Weak and viscosity solutions -Maximum principles and barriers -Moving plane method -Bernstein's technique -Schauder estimates (review) -De Giorgi-Nash-Moser and Hölder continuity of gradients |

Literature | Elliptic Partial Differential Equations: Second Edition Qing Han and Fanghua Lin Publication Year: 2011 ISBN-10: 0-8218-5313-9 ISBN-13: 978-0-8218-5313-9 Courant Lecture Notes, vol. 1.R |

Prerequisites / Notice | Although many parts of the book are rather self-contained, it would be advisable to have followed before the bachelor course Functional Analysis II |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | J. Serra |

Type | ungraded semester performance |

Language of examination | English |

Repetition | Repetition only possible after re-enrolling for the course unit. |

### Learning materials

No public learning materials available. | |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

Places | Limited number of places. Special selection procedure. |

Beginning of registration period | Registration possible from 04.01.2021 |

Priority | Registration for the course unit is only possible for the primary target group |

Primary target group | Mathematics BSc (404000)
starting semester 06 Mathematics MSc (437000) Applied Mathematics MSc (437100) |

Waiting list | until 01.03.2021 |

End of registration period | Registration only possible until 19.02.2021 |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mathematics Bachelor | Seminars | W | |

Mathematics Master | Seminars | W |