This course will mainly deal with linear partial differential equations (PDE), and will build in particular on the material of the course Partial Differential Equations I as taught in the summer semesters of 2011, 2013, 2015, 2017 and 2019. The content is a selection of the following:

• Weak solutions; existence, regularity, eigenvalues and eigenfunctions
• Theory of linear elliptic partial differential equations.
• Classical solutions; Schauder theory.
• Maximum and comparison principles.
• De Giorgi – Nash theorem
• Leray-Schauder theory; existence and regularity of solutions.

Prerequisites: Partial Differential Equations I