# 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. |

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 |

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 |