Optimal Regularity and the Free Boundary in The Parabolic Signorini Problem
Presenter
January 14, 2011
Keywords:
- partial differential equations
- applied PDE
- boundary layers and boundary conditions
- Signorini problem
- linear elasticity
- static equilibrium solutions
MSC:
- 35R35
- 35R37
- 35-xx
- 35Qxx
- 74Bxx
- 74B10
- 74B15
- 37D35
- 35Q74
Abstract
In this talk we present a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's - and Poon's - monotonicity formula for the frequency. Our main result include the proof of the optimal regularity of solutions, the classification of free boundary points, the regularity of the regular set, and the structure of the singular set. This is joint work with N. Garofalo, A. Petrosyan, and T. To.