A total of 4 lectures by the course leader will be given. Examination:  The examination will consist of two parts: Home work assignments 2h lecture of a suggested topic Literature:    http://www.ams.org/bookstore-getitem/item=gsm-136

Regularity Theory of Free Boundaries

Spring 2013

A Partially Self study course

 
 
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Course Leader:

Henrik Shahgholian          08-790 6754 henriksh@math.kth.se


Start:  Monday  January 14,   13.15-15.00, at room 3733, Building of the  Dept. of Mathematics.


Language:   English


Goal:  To learn basics of the regularity theory in free boundary problems of obstacle type.

Prerequisites:  Some knowledge in PDE.  Good knowledge in Analysis.

Topics

Weak and viscosity solutions, elliptic estimates, compactness, maximum principle, Liouville's theorem, Hausdorff measure.

Applications: A catalog of FBP 

Obstacle problem, harmonic continuation, composite membrane, two-phase membrane problem, superconductivity. 

Monotonicity Formulas:

We will discuss two main monotonicity formulas that constitute basic tools.

Free Boundary Regularity:

Optimal regularity of the solutions, non-degeneracy, Hausdorff measure of the free boundary, classification of global solutions, local regularity of the free boundary.