Year: 2017
Type: preprint
Abstract: In this paper, we prove local $C^{1}$ regularity of free boundaries for the double obstacle problem with an upper obstacle $ψ$, \begin{align*} Δu &=fχ_{Ω(u) \cap\{ u< ψ\} }+ Δψχ_{Ω(u)\cap \{u=ψ\}}, \qquad u\le ψ\quad \text { in } B_1, \end{align*} where $Ω(u)=B_1 \setminus \left( \{u=0\} \cap \{ \nabla u =0\}\right)$ under a thickness assumption for $u$ and $ψ$.
Source: arXiv (Cornell University)
Authors: Lee, Ki-ahm, Park, Jinwan, Shahgholian, Henrik
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953159128