The aim of this course is to illustrate ideas relevant in the theory of existence and regularity of linear partial differential equations. The focus will be the so called L^2 theory. This theory provides a relative robust approach to deal with elliptic differential equations, parabolic equations and even hyperbolic equations in divergence form.  

Prerequisites are Analysis I,II and Measure theory. Functional Analysis 1 and the content of PDE 1 will be helpful.

As reference we will use (beside others) mainly the book by C.Evans, Partial Differential Equations. 

I am looking forward to welcoming you in my course. 

Semester: ST 2020