Optimal regularity and the study of the free boundary in the parabolic Signorini problem
Presenter
March 8, 2011
Keywords:
- applied PDE
- partial differential equations
- electrostatics
- boundary layers and boundary conditions
- ill-posedness
- thin obstacle problem
MSC:
- 35R35
- 35R37
- 35-xx
- 35Qxx
- 74B05
- 35Q60
Abstract
I will survey some recent joint work with D. Danielli, A. Petrosyan and T. To. We give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency to parabolic equations. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.