Regularity Theory of Free Boundaries
Spring 2013
A Partially Self study course
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.