Blow up analysis for a parabolic MEMS problem, I: H\'{o}lder estimate
- Resource Type
- Working Paper
- Authors
- Wang, Kelei; Yi, Guangzeng
- Source
- Subject
- Mathematics - Analysis of PDEs
35K58, 35B44, 35B45
- Language
This is the first in a series of papers devoted to the blow up analysis for the quenching phenomena in a parabolic MEMS equation. In this paper, we first give an optimal H\"{o}lder estimate for solutions to this equation by using the blow up method and some Liouville theorems on stationary two-valued caloric functions, and then establish a convergence theory for sequences of uniformly H\"{o}lder continuous solutions. These results are also used to prove a stratification theorem on the rupture set $\{u=0\}$.
Comment: 34 pages. Comments welcome