In this course I will discuss the basics of the classical theory of free boundary problems. We will focus on two problems; the Alt-Caffarelli and obstacle problem. In the first part of the course we will discuss the regularity of the solutions, and in the remainder the full and partial regularity of the free boundary.
A.Karakhanyan is a Professor at the University of Edinburgh. He has obtained his PhD from KTH in Stockholm. Before moving to the UK he worked as an ARC research fellow in The Australian National University in Canberra, and as an Instructor at The University of Texas at Austin. His main research interests include nonlinear partial differential equations, free boundary problems and geometric analysis.