Year: 2026
Type: preprint
Abstract: In the pioneer work of vectorial free boundary problems \cite[Adv. Math. 280 (2015)]{ASUW15}, Andersson, Shahgholian, Uraltseva, and Weiss investigated the regularity theory of solutions and the free boundary of a singular cooperative system \begin{equation*} Δ\mathbf{u} = \frac{\mathbf{u}}{|\mathbf{u}|} χ_{\{|\mathbf{u}|>0\}} \quad\text{in }Ω\subset\mathbb{R}^n, \qquad \mathbf{u}:Ω\longrightarrow \mathbb{R}^m, \qquad n,m\ge 2. \end{equation*} At the level of solutions, the boundedness of the right-hand side directly yields $W^{2,p}_{\mathrm{loc}}$ regularity for every $1
Source: arXiv (Cornell University)
Authors: Du, Lili, Tang, Xu, Wang, Cong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213289006